You are encouraged to solve this task according to the task description, using any language you may know.

The Harshad or Niven numbers are positive integers ≥ 1 that are divisible by the sum of their digits.

For example,   42   is a Harshad number as   42   is divisible by   (4 + 2)   without remainder.
Assume that the series is defined as the numbers in increasing order.

The task is to create a function/method/procedure to generate successive members of the Harshad sequence.

Use it to list the first twenty members of the sequence and list the first Harshad number greater than 1000.

function Next(N: in out Positive) return Positive is

function Sum_Of_Digits(N: Natural) return Natural is
( if N = 0 then 0 else ((N mod 10) + Sum_Of_Digits(N / 10)) );

begin
while not (N mod Sum_Of_Digits(N) = 0) loop
N := N + 1;
end loop;
return N;
end Next;

Current: Positive := 1;

begin
for I in 1 .. 20 loop
Current := Current + 1;
end loop;
Current := 1000 + 1;
Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 ... 1002

ALGOL 68

BEGIN
PROC digit sum = (INT i) INT :
BEGIN
INT res := i %* 10, h := i;
WHILE (h %:= 10) > 0 DO res +:= h %* 10 OD;
res
END;
INT found := 0;
FOR i WHILE found < 20 DO
(i %* digit sum (i) = 0 | found +:= 1; printf (($g(0)", "$, i)) ) OD;
FOR i FROM 1001 DO
(i %* digit sum (i) = 0 | printf (($g(0)l$, i)); stop) OD
END
Output:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 1002

AutoHotkey

H := []
n := 1

Loop
n := (H[A_Index] := NextHarshad(n)) + 1
until H[H.MaxIndex()] > 1000

Loop, 20
Out .= H[A_Index] ", "

MsgBox, % Out ". . . " H[H.MaxIndex()]

Loop, {
Loop, Parse, n
sum += A_LoopField
if (!Mod(n, sum))
return n
n++, sum := ""
}
}
Output:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, . . . 1002

AWK

#!/usr/bin/awk -f
BEGIN {
k=0; n=0;
printf("First twenty Harshad numbers are:\n ");
while (k<20) {
printf("%i ",n);
++k;
}
}
n = 1000;
printf("\nFirst Harshad number larger than 1000 is \n  %i\n",n);
}

s = 0;
for (i=0; i<length(n); ) {
s+=substr(n,++i,1);
}
return !(n%s);
}
Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42
First Harshad number larger than 1000 is
1002

Batch File

@echo off
setlocal enabledelayedexpansion

for /l %%i in (1,1,20) do (
echo Harshad number %%i - !errorlevel!
)

:loop
if %errorlevel% leq 1000 goto loop
echo First Harshad number greater than 1000: %errorlevel%
pause>nul
exit /b

:strlength
setlocal enabledelayedexpansion
set tempcount=1
set str=%1
:strlengthloop
set /a length=%tempcount%-1
if "!str:~%tempcount%,1!"=="" endlocal && exit /b %length%
set /a tempcount+=1
goto strlengthloop

Output:
First Harshad number greater than 1000: 1002

BBC BASIC

I%=1:CNT%=0
WHILE TRUE
IF CNT%<20 PRINT ;I%;" ";:CNT%+=1
IF I%>1000 PRINT ;I%:EXIT WHILE
ENDIF
I%+=1
ENDWHILE
END

LOCAL sum%,tmp%
tmp%=num%
sum%=0
WHILE (tmp%>0)
sum%+=tmp% MOD 10
tmp%/=10
ENDWHILE
=(num% MOD sum%)=0
Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002

Befunge

45*1>::01-\>:55+%\vv\0<
>\1+^ + <|:/<+55<  :
^_>1-\:[email protected]>\:0\#v_+\^
>^1\,+55<.^_:#%$:#<"}"v ^!:\_ ^###< !*8< Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 C #include <stdio.h> static int digsum(int n) { int sum = 0; do { sum += n % 10; } while (n /= 10); return sum; } int main(void) { int n, done, found; for (n = 1, done = found = 0; !done; ++n) { if (n % digsum(n) == 0) { if (found++ < 20) printf("%d ", n); if (n > 1000) done = printf("\n%d\n", n); } } return 0; } Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 C# using System; using System.Collections.Generic; namespace Harshad { class Program { public static bool IsHarshad(int n) { char[] inputChars = n.ToString().ToCharArray(); IList<byte> digits = new List<byte>(); foreach (char digit in inputChars) { digits.Add((byte)Char.GetNumericValue(digit)); } if (n < 1) { return false; } int sum = 0; foreach (byte digit in digits) { sum += digit; } return n % sum == 0; } static void Main(string[] args) { int i = 1; int count = 0; while (true) { if (IsHarshad(i)) { count++; if (count <= 20) { Console.Write(string.Format("{0} ", i)); } else if (i > 1000) { Console.Write(string.Format("{0} ", i)); break; } } i++; } Console.ReadKey(); } } } Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 C++ #include <vector> #include <iostream> int sumDigits ( int number ) { int sum = 0 ; while ( number != 0 ) { sum += number % 10 ; number /= 10 ; } return sum ; } bool isHarshad ( int number ) { return number % ( sumDigits ( number ) ) == 0 ; } int main( ) { std::vector<int> harshads ; int i = 0 ; while ( harshads.size( ) != 20 ) { i++ ; if ( isHarshad ( i ) ) harshads.push_back( i ) ; } std::cout << "The first 20 Harshad numbers:\n" ; for ( int number : harshads ) std::cout << number << " " ; std::cout << std::endl ; int start = 1001 ; while ( ! ( isHarshad ( start ) ) ) start++ ; std::cout << "The smallest Harshad number greater than 1000 : " << start << '\n' ; return 0 ; } Output: The first 20 Harshad numbers: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 The smallest Harshad number greater than 1000 : 1002 Clojure (defn digsum [n acc] (if (zero? n) acc (digsum (quot n 10) (+ acc (mod n 10))))) (let [harshads (filter #(zero? (mod % (digsum % 0))) (iterate inc 1))] (prn (take 20 harshads)) (prn (first (filter #(> % 1000) harshads)))) Output: (1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42) 1002 COBOL Works with: OpenCOBOL version 1.1 identification division. program-id. harshad. environment division. data division. working-storage section. *> for storing first 20 harshad-niven numbers 01 harshads. 03 harshad pic 9(5) occurs 20 times indexed by niven. *> numbers tested for harshad-niven-ness. 01 first-num pic 9(5). 01 second-num pic 9(5). *> loop counter 01 i pic 9(5). *> for calculating sum of digits 01 div pic 9(5). 01 mod pic 9(5). 01 tot pic 9(5). *> for harshad-niven calculation and display 01 harshad-div pic 9(5). 01 harshad-mod pic 9(5). 88 evenly-divisible value 0. 01 harshad-disp pic zzzz9. 01 harshad-result pic 9(5). *> for selecting what to do with results of harshad calculation 01 pass pic 9. 88 first-pass value 1. 88 second-pass value 2. procedure division. 10-main section. move 1 to pass. set niven to 1. perform 20-calculate-harshad with test before varying first-num from 1 by 1 until niven = 21. move 2 to pass. move first-num to second-num. perform 20-calculate-harshad with test after varying first-num from second-num by 1 until harshad-result > 1000. perform with test after varying i from 1 by 1 until i = 20 move harshad(i) to harshad-disp display function trim(harshad-disp) space with no advancing end-perform. move harshad-result to harshad-disp. display "... " function trim(harshad-disp). stop run. 20-calculate-harshad. move first-num to div. move zero to harshad-result. perform 100-calculate-sum-of-digits. divide first-num by tot giving harshad-div remainder harshad-mod. if evenly-divisible if first-pass move first-num to harshad(niven) set niven up by 1 else move first-num to harshad-result end-if end-if. exit paragraph. 100-calculate-sum-of-digits. move zero to tot. perform with test after until div = 0 divide div by 10 giving div remainder mod add mod to tot end-perform. *> if tot >= 10 *> move tot to div *> go to 100-calculate-sum-of-digits *> end-if. exit paragraph. ColdFusion <Cfset harshadNum = 0> <Cfset counter = 0> <Cfloop condition="harshadNum lte 1000"> <Cfset startnum = harshadNum + 1> <Cfset digits = 0> <Cfset harshad = 0> <Cfloop condition="Harshad eq 0"> <Cfset current_i = startnum> <Cfset digits = 0> <cfloop condition="len(current_i) gt 1"> <Cfset digit = left(current_i, 1)> <Cfset current_i = right(current_i, len(current_i)-1)> <Cfset digits = digits + digit> </cfloop> <Cfset digits = digits + current_i> <Cfif Startnum MOD digits eq 0> <Cfset harshad = 1> <Cfelse> <cfset startnum = startnum + 1> </Cfif> </Cfloop> <cfset harshadNum = startnum> <Cfset counter = counter + 1> <Cfif counter lte 20> <Cfoutput>#harshadNum# </Cfoutput> </Cfif> </Cfloop> <Cfoutput>... #harshadNum# </Cfoutput> Common Lisp (defun harshadp (n) (zerop (rem n (digit-sum n)))) (defun digit-sum (n &optional (a 0)) (cond ((zerop n) a) (t (digit-sum (floor n 10) (+ a (rem n 10)))))) (defun list-harshad (n &optional (i 1) (lst nil)) "list the first n Harshad numbers starting from i (default 1)" (cond ((= (length lst) n) (reverse lst)) ((harshadp i) (list-harshad n (+ i 1) (cons i lst))) (t (list-harshad n (+ i 1) lst)))) Output: CL-USER> (list-harshad 20) (1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42) CL-USER> (list-harshad 1 1001) (1002) D void main() { import std.stdio, std.algorithm, std.range, std.conv; enum digSum = (int n) => n.text.map!(d => d - '0').sum; enum harshads = iota(1, int.max).filter!(n => n % digSum(n) == 0); harshads.take(20).writeln; harshads.filter!(h => h > 1000).front.writeln; } Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42] 1002 EchoLisp (define (harsh? n) (zero? (modulo n (apply + (map string->number (string->list (number->string n))))))) (harsh? 42) → #t (define H (stream-filter harsh? (in-naturals 1))) (take H 20) (1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42) (for ((n H)) #:break (> n 1000) => n) 1002 Eiffel note description : "project application root class" date : "$October 10, 2014$" revision : "$Revision$" class NIVEN_SERIES create make feature make local number : INTEGER count : INTEGER last : BOOLEAN do number := 1 from number := 1 last := false until last = true loop if (number \\ sum_of_digits(number) = 0) then count := count + 1 if (count <= 20 ) then print("%N") print(number) end if (number > 1000) then print("%N") print(number) last := true end end number := number + 1 end end sum_of_digits(no:INTEGER):INTEGER local sum : INTEGER num : INTEGER do sum := 0 from num := no until num = 0 loop sum := sum + num \\ 10 num := num // 10 end Result := sum end end Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 Elixir defmodule Harshad do def series, do: Stream.iterate(1, &(&1+1)) |> Stream.filter(&(number?(&1))) def number?(n), do: rem(n, digit_sum(n, 0)) == 0 defp digit_sum(0, sum), do: sum defp digit_sum(n, sum), do: digit_sum(div(n, 10), sum + rem(n, 10)) end IO.inspect Harshad.series |> Enum.take(20) IO.inspect Harshad.series |> Stream.drop_while(&(&1 <= 1000)) |> Enum.take(1) |> hd Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42] 1002 Erlang -module( harshad ). -export( [greater_than/1, sequence/1, task/0] ). greater_than( N ) when N >= 1 -> greater_than( 2, N, acc(1, {0, []}) ). sequence( Find_this_many ) when Find_this_many >= 1 -> sequence( 2, Find_this_many, acc(1, {0, []}) ). task() -> io:fwrite( "~p~n", [sequence(20)] ), io:fwrite( "~p~n", [greater_than(1000)] ). acc( N, Acc ) -> acc( N rem lists:sum([X -$0|| X <- erlang:integer_to_list(N)]), N, Acc ).

acc( 0, N, {Found, Acc} ) -> {Found + 1, [N | Acc]};
acc( _Reminder, _N, Acc ) -> Acc.

greater_than( _N, Find, {_, [Found | _T]} ) when Found > Find -> Found;
greater_than( N, Find, Acc ) -> greater_than( N + 1, Find, acc(N, Acc) ).

sequence( _N, Found, {Found, Acc} ) -> lists:reverse( Acc );
sequence( N, Find, Acc ) -> sequence( N + 1, Find, acc(N, Acc) ).

Output:
[1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42]
1002

Erlang 2

A somewhat more simple approach. Somewhat more efficient since it produces the partial list 23 times for the 20 element case whereas the above does so 36 or 37 times.

% We return the number R if harshad, else 0
case R
rem lists:sum([X - $0|| X <- erlang:integer_to_list(R)]) of 0 -> R; _ -> 0 end. % build a list of harshads retrieving input from harshad(R) % filter out the nulls and return hlist(A,B) -> RL = [ harshad(X) || X <- lists:seq(A,B) ], lists:filter( fun(X) -> X > 0 end, RL). seq(Total) -> seq(Total, [], 0). seq(Total,L,_) when length(L) == Total-> L; seq(Total,L,Acc) when length(L) < Total -> NL = hlist(1,Total + Acc), seq(Total,NL,Acc+1). gt(_,L) when length(L) == 1 -> hd(L); gt(X,_) -> NL = hlist(X+1,X+2), gt(X+2,NL). main() -> io:format("seq(20): ~w~n", [ seq(20) ]), io:format("gt(1000): ~w~n", [ gt(1000,[]) ]). 2> harshad:main(). seq(20): [1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42] gt(1000): 1002 ok F# let divides d n = match bigint.DivRem(n, d) with | (_, rest) -> rest = 0I let splitToInt (str:string) = List.init str.Length (fun i -> ((int str.[i]) - (int "0".[0]))) let harshads = let rec loop n = seq { let sum = List.fold (+) 0 (splitToInt (n.ToString())) if divides (bigint sum) n then yield n yield! loop (n + 1I) } loop 1I [<EntryPoint>] let main argv = for h in (Seq.take 20 harshads) do printf "%A " h printfn "" printfn "%A" (Seq.find (fun n -> n > 1000I) harshads) 0 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 Factor USING: math.text.utils lists lists.lazy ; : niven? ( n -- ? ) dup 1 digit-groups sum mod 0 = ; : first-n-niven ( n -- seq ) 1 lfrom [ niven? ] lfilter ltake list>array ; : next-niven ( n -- m ) 1 + [ dup niven? ] [ 1 + ] until ; 20 first-n-niven . 1000 next-niven . Output: { 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 } 1002 FBSL The INITIALIZE routine fills a dynamic array with all we need, even the ellipsis. #APPTYPE CONSOLE CLASS harshad PRIVATE: memo[] SUB INITIALIZE() DIM i = 1, c DO IF isNiven(i) THEN c = c + 1 memo[c] = i END IF i = i + 1 IF c = 20 THEN EXIT DO LOOP memo[] = "..." i = 1000 WHILE NOT isNiven(INCR(i)): WEND memo[] = i END SUB FUNCTION isNiven(n) RETURN NOT (n MOD sumdigits(n)) END FUNCTION FUNCTION sumdigits(n) DIM num = n, m, sum WHILE num sum = sum + num MOD 10 num = num \ 10 WEND RETURN sum END FUNCTION PUBLIC: METHOD Yield() FOREACH DIM e IN memo PRINT e, " "; NEXT END METHOD END CLASS DIM niven AS NEW harshad niven.Yield() PAUSE Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 ... 1002 Press any key to continue... Fortran Please observe compilation on GNU/linux system and output from run are in the comments at the START of the FORTRAN 2003 source. The 1--20 loop idea was stolen from the ada solution. Thank you. !-*- mode: compilation; default-directory: "/tmp/" -*- !Compilation started at Tue May 21 13:15:59 ! !a=./f && make$a && $a < unixdict.txt !gfortran -std=f2003 -Wall -ffree-form f.f03 -o f ! 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 ! !Compilation finished at Tue May 21 13:15:59 program Harshad integer :: i, h = 0 do i=1, 20 call nextHarshad(h) write(6, '(i5)', advance='no') h enddo h = 1000 call nextHarshad(h) write(6, '(i5)') h contains subroutine nextHarshad(h) ! alter input integer h to be the next greater Harshad number. integer, intent(inout) :: h h = h+1 ! bigger do while (.not. isHarshad(h)) h = h+1 end do end subroutine nextHarshad logical function isHarshad(a) integer, intent(in) :: a integer :: mutable, digit_sum isHarshad = .false. if (a .lt. 1) return ! false if a < 1 mutable = a digit_sum = 0 do while (mutable /= 0) digit_sum = digit_sum + mod(mutable, 10) mutable = mutable / 10 end do isHarshad = 0 .eq. mod(a, digit_sum) end function isHarshad end program Harshad FreeBASIC ' FB 1.05.0 Win64 Function sumDigits(n As Integer) As Integer If n < 0 Then Return 0 Dim sum As Integer While n > 0 sum += n Mod 10 n \= 10 Wend Return sum End Function Function isHarshad(n As Integer) As Boolean Return n Mod sumDigits(n) = 0 End Function Print "The first 20 Harshad or Niven numbers are :" Dim count As Integer = 0 Dim i As Integer = 1 Do If isHarshad(i) Then Print i; " "; Count += 1 If count = 20 Then Exit Do End If i += 1 Loop Print : Print Print "The first such number above 1000 is :" i = 1001 Do If isHarshad(i) Then Print i; " " Exit Do End If i += 1 Loop Print Print "Press any key to quit" Sleep Output: The first 20 Harshad or Niven numbers are : 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 The first such number above 1000 is : 1002 Frink isHarshad[n] := n mod sum[integerDigits[n]] == 0 c = 0 i = 1 while c<20 { if isHarshad[i] { c = c + 1 println[i] } i = i + 1 } println[] i = 1000 do i = i + 1 while ! isHarshad[i] println[i] Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 Gambas Public Sub Main() Dim siCount, siLoop, siTotal, siCounter As Short Dim sNo, sTemp As String Dim sHold, sNiven As New String[] For siCount = 1 To 1500 sNo = Str(siCount) For siLoop = 1 To Len(sNo) sHold.Add(Mid(sNo, siLoop, 1)) Next For Each sTemp In sHold siTotal += Val(sTemp) Next If siCount Mod siTotal = 0 Then Inc siCounter If siCounter < 21 Or siCount > 1000 Then sNiven.Add(Str(siCount)) If siCount > 1000 Then Break Endif Endif siTotal = 0 sHold.Clear Next Print "First twenty Harshad numbers and the first Harshad number greater than 1000" Print sNiven.Join(", ") End Output: First twenty Harshad numbers and the first Harshad number greater than 1000 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 1002 Go package main import "fmt" type is func() int func newSum() is { var ms is ms = func() int { ms = newSum() return ms() } var msd, d int return func() int { if d < 9 { d++ } else { d = 0 msd = ms() } return msd + d } } func newHarshard() is { i := 0 sum := newSum() return func() int { for i++; i%sum() != 0; i++ { } return i } } func main() { h := newHarshard() fmt.Print(h()) for i := 1; i < 20; i++ { fmt.Print(" ", h()) } fmt.Println() h = newHarshard() n := h() for ; n <= 1000; n = h() { } fmt.Println(n) } Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 Groovy class HarshadNiven{ public static boolean find(int x) { int sum = 0,temp,var; var = x; while(x>0) { temp = x%10; sum = sum + temp; x = x/10; } if(var%sum==0) temp = 1; else temp = 0; return temp; } public static void main(String[] args) { int t,i; t = 0; for(i=1;t<20;i++) { if(find(i)) { print(i + " "); t++; } } int x = 0; int y = 1000; while(x!=1) { if(find(y)) x = 1; y++; } println(); println(y+1); } } Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 Haskell import Data.Char (ord) harshads :: [Int] harshads = let digsum = sum . map ((48 -) . ord) . show in filter ((0 ==) . (mod <*> digsum)) [1 ..] main :: IO () main = mapM_ print [take 20 harshads, [(head . filter (> 1000)) harshads]] Output: [1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42] 1002 Or, as an alternative to strings and imports: harshadSeries :: [Int] harshadSeries = filter ((0 ==) . (rem <*> (sum . digitList))) [1 ..] digitList :: Int -> [Int] digitList 0 = [] digitList n = rem n 10 : digitList (quot n 10) main :: IO () main = mapM_ print$ [take 20, take 1 . dropWhile (<= 1000)] <*> [harshadSeries]
Output:
[1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42]
[1002]

Icon and Unicon

procedure main(A)
limit := integer(A[1]) | 20
every writes(niven(seq())\limit," ")
writes("... ")
write(niven(seq(1001))\1)
end

procedure niven(n)
n ? {s := 0; while s +:= move(1)}
if (n%s) = 0 then return n
end
Output:
->ns
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 ... 1002
->

J

Until =: 2 : 'u^:([email protected]:v)^:_'
isHarshad =: 0 = ] |~ [: +/ #.inv NB. BASE isHarshad N
assert 1 0 -: 10 isHarshad&> 42 38
assert 3 4 5 -: nextHarshad&> 2 3 4
assert 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 -: (, [email protected]:{:)Until (20 = #) 1

NB. next Harshad number in base 6. Input and output are in base 6.
NB. Verification left to you, gentle programmer.
23253

Java

Works with: Java version 1.5+
private static long sumDigits(long n){
long sum = 0;
for(char digit:Long.toString(n).toCharArray()){
sum += Character.digit(digit, 10);
}
return sum;
}
public static void main(String[] args){
for(int count = 0, i = 1; count < 20;i++){
if(i % sumDigits(i) == 0){
System.out.println(i);
count++;
}
}
System.out.println();
for(int i = 1001; ; i++){
if(i % sumDigits(i) == 0){
System.out.println(i);
break;
}
}
}
}
Output:
1
2
3
4
5
6
7
8
9
10
12
18
20
21
24
27
30
36
40
42

1002

JavaScript

ES5

var s = 0;
var n_str = new String(n);
for (var i = 0; i < n_str.length; ++i) {
s += parseInt(n_str.charAt(i));
}
return n % s === 0;
}

var count = 0;

for (var n = 1; count < 20; ++n) {
count++;
}
}

var h = 1000;
console.log(h);

Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42
1002

ES6

One possible approach to functional composition:

(() => {
'use strict';

// nHarshads :: Int -> [Int]
const nHarshads = n => {

// isHarshad :: Int -> Bool
const isHarshad = n => 0 === n % sum(digitList(n));

return until(
dct => dct.nth === n,
dct => {
const
next = succ(dct.i),
return {
i: next,
hs: blnHarshad ? dct.hs.concat(next) : dct.hs,
nth: dct.nth + (blnHarshad ? 1 : 0)
};
}, {
i: 0,
hs: [],
nth: 0
}
)
.hs;
};

// GENERIC FUNCTIONS ------------------------------------------------------

// digitList :: Int -> [Int]
const digitList = n =>
n > 0 ? [n % 10].concat(digitList(Math.floor(n / 10))) : [];

// dropWhile :: (a -> Bool) -> [a] -> [a]
const dropWhile = (p, xs) => {
let i = 0;
for (let lng = xs.length;
(i < lng) && p(xs[i]); i++) {}
return xs.slice(i);
};

// head :: [a] -> a
const head = xs => xs.length ? xs[0] : undefined;

// a -> String
const show = x => JSON.stringify(x, null, 2);

// succ :: Int -> Int
const succ = x => x + 1

// sum :: (Num a) => [a] -> a
const sum = xs => xs.reduce((a, x) => a + x, 0);

// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = (p, f, x) => {
const go = x => p(x) ? x : go(f(x));
return go(x);
};

// TEST -------------------------------------------------------------------
return show({
});
})();
Output:
{
"firstTwenty": [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
12,
18,
20,
21,
24,
27,
30,
36,
40,
42
],
"firstOver1000": 1002
}

jq

def digits: tostring | [explode[] | ([.]| implode) | tonumber];
if . >= 1 then (. % (digits|add)) == 0
else false
end ;

# produce a stream of n Harshad numbers
# [candidate, count]
elif .[1] > 0 then [.[0]+1, .[1]] | _harshads
else empty
end;

# First Harshad greater than n where n >= 0
# input: next candidate
end;

Output:
$jq -n -c -f harshad.jq [1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42,"...",1002] Julia Works with: Julia version 0.6 isharshad(x) = x % sum(digits(x)) == 0 nextharshad(x) = begin while !isharshad(x+1) x += 1 end; return x + 1 end function harshads(n::Integer) h = Vector{typeof(n)}(n) h[1] = 1 for j in 2:n h[j] = nextharshad(h[j-1]) end return h end println("First 20 harshad numbers: ", join(harshads(20), ", ")) println("First harshad number after 1001: ", nextharshad(1000)) Output: First 20 harshad numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42 First harshad number after 1001: 1002 K / sum of digits of an integer sumdig: {d::(); (0<){d::d,x!10; x%:10}/x; +/d} / Test if an integer is a Harshad number isHarshad: {:[x!(sumdig x); 0; 1]} / Returns 1 if Harshad / Generate x Harshad numbers starting from y and display the list hSeries: {harshad::();i:y;while[(x-#harshad)>0;:[isHarshad i; harshad::(harshad,i)]; i+:1];harshad} Output: hSeries[20;1] 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 hSeries[1; 1001] ,1002 Kotlin // version 1.1 fun sumDigits(n: Int): Int = when { n <= 0 -> 0 else -> { var sum = 0 var nn = n while (nn > 0) { sum += nn % 10 nn /= 10 } sum } } fun isHarshad(n: Int): Boolean = (n % sumDigits(n) == 0) fun main(args: Array<String>) { println("The first 20 Harshad numbers are:") var count = 0 var i = 0 while (true) { if (isHarshad(++i)) { print("$i ")
if (++count == 20) break
}
}

println("\n\nThe first Harshad number above 1000 is:")
i = 1000

while (true) {
println(i)
return
}
}
}
Output:
The first 20 Harshad numbers are:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42

The first Harshad number above 1000 is:
1002

LOLCODE

HAI 1.3

HOW IZ I digsummin YR num
I HAS A digsum ITZ 0
IM IN YR LOOP
num, O RLY?
YA RLY
digsum R SUM OF digsum AN MOD OF num AN 10
num R QUOSHUNT OF num AN 10
NO WAI, FOUND YR digsum
OIC
IM OUTTA YR LOOP
IF U SAY SO

I HAS A found ITZ 0

IM IN YR finder UPPIN YR n
I HAS A n ITZ SUM OF n AN 1
I HAS A digsum ITZ I IZ digsummin YR n MKAY

NOT MOD OF n AN digsum, O RLY?
YA RLY
DIFFRINT found AN BIGGR OF found AN 20, O RLY?
YA RLY
VISIBLE n " "!
found R SUM OF found AN 1
OIC

DIFFRINT n AN SMALLR OF n AN 1000, O RLY?
YA RLY, VISIBLE ":)" n, GTFO
OIC
OIC
IM OUTTA YR finder

KTHXBYE
Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42
1002

Lua

local s=0
local n_str=tostring(n)
for i=1,#n_str do
s=s+tonumber(n_str:sub(i,i))
end
return n%s==0
end

local count=0
local n=1

while count<20 do
count=count+1
end
n=n+1
end

local h=1001
h=h+1
end
print(h)

Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42
1002

Mathematica / Wolfram Language

NestWhile[# + 1 &, # + 1, ! Divisible[#, [email protected]@#] &] &;
[email protected]@1000;
Output:
{1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42}
1002

MATLAB / Octave

Define a testing function whether n is harshad or not

v = isinteger(n) && ~mod(n,sum(num2str(n)-'0'));
end;

Check numbers

k=1; n=1;
while (k<=20)
printf('%i ',n);
k=k+1;
end;
n=n+1;
end
n = 1001;
n=n+1;
end;
printf('\nFirst harshad number larger than 1000 is %i\n',n);
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42
First harshad number larger than 1000 is 1002

MLite

fun sumdigits
(0, n) = n
| (m, n) = sumdigits (m div 10, m rem 10) + n
| n = sumdigits (n div 10, n rem 10)

fun is_harshad n = (n rem (sumdigits n) = 0)

(n, ~1) = if is_harshad n then
n
else
| n = next_harshad_after (n + 1, ~1)

(max, _, count > max, accum) = rev accum
| (max, here, count, accum) =
harshad (max, here + 1, count + 1, here :: accum)
else
harshad (max, here + 1, count, accum)
| max = harshad (max, 1, 1, [])

;

print "first harshad number after 1000 = "; println ` next_harshad_after 1000;

NetRexx

/* NetRexx ------------------------------------------------------------
* 21.01.2014 Walter Pachl translated from ooRexx (from REXX version 1)
*--------------------------------------------------------------------*/

options replace format comments java crossref symbols nobinary

Parse Arg x y . /* get optional arguments: X Y */
If x='' Then x=20 /* Not specified? Use default */
If y='' Then y=1000 /* " " " " */
n=0 /* Niven count */
nl='' /* Niven list. */

Loop j=1 By 1 Until n=x /* let's go Niven number hunting.*/
If j//sumdigs(j)=0 Then Do /* j is a Niven number */
n=n+1 /* bump Niven count */
nl=nl j /* add to list. */
End
End

Say 'first' n 'Niven numbers:'nl

If j//sumdigs(j)=0 Then /* j is a Niven number */
Leave
End

Say 'first Niven number >' y 'is:' j
Exit

method sumdigs(n) public static returns Rexx
sum=n.left(1)
Loop k=2 To n.length()
sum=sum+n.substr(k,1)
End
Return sum

output same as ooRexx's

Nim

import strutils

proc slice[T](iter: iterator(): T {.closure.}, sl): seq[T] =
var result {.gensym.}: seq[int64] = @[]
var i = 0
for n in iter():
if i > sl.b:
break
if i >= sl.a:
inc i
result

for n in 1 .. < int64.high:
var sum = 0
for ch in string($n): sum += parseInt("" & ch) if n mod sum == 0: yield n echo harshad.slice 0 .. <20 for n in harshad(): if n > 1000: echo n break Output: @[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42] 1002 Objeck class Harshad { function : Main(args : String[]) ~ Nil { count := 0; for(i := 1; count < 20; i += 1;) { if(i % SumDigits(i) = 0){ "{$i} "->Print();
count += 1;
};
};

for(i := 1001; true; i += 1;) {
if(i % SumDigits(i) = 0){
"... {$i}"->PrintLine(); break; }; }; } function : SumDigits(n : Int) ~ Int { sum := 0; do { sum += n % 10; n /= 10; } while(n <> 0); return sum; } } 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 ... 1002 Oforth : sumDigits(n) 0 while(n) [ n 10 /mod ->n + ] ; : isHarshad dup sumDigits mod 0 == ; 1100 seq filter(#isHarshad) dup left(20) println dup filter(#[ 1000 > ]) first println Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42] 1002 ooRexx /* REXX --------------------------------------------------------------- * 21.01.2014 Walter Pachl modi-(simpli-)fied from REXX version 1 *--------------------------------------------------------------------*/ Parse Arg x y . /* get optional arguments: X Y */ If x='' Then x=20 /* Not specified? Use default */ If y='' Then y=1000 /* " " " " */ n=0 /* Niven count */ nl='' /* Niven list. */ Do j=1 Until n=x /* let's go Niven number hunting.*/ If j//sumdigs(j)=0 Then Do /* j is a Niven number */ n=n+1 /* bump Niven count */ nl=nl j /* add to list. */ End End Say 'first' n 'Niven numbers:'nl Do j=y+1 /* start with first candidate */ If j//sumdigs(j)=0 Then /* j is a Niven number */ Leave End Say 'first Niven number >' y 'is:' j Exit sumdigs: Procedure /* compute sum of n's digits */ Parse Arg n sum=left(n,1) Do k=2 To length(n) sum=sum+substr(n,k,1) End Return sum Output: first 20 Niven numbers: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 first Niven number > 1000 is: 1002 PARI/GP Works with: PARI/GP version 2.6.0 and above isHarshad(n)=n%sumdigits(n)==0 n=0;k=20;while(k,if(isHarshad(n++),k--;print1(n", "))); n=1000;while(!isHarshad(n++),);print("\n"n) Output: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 1002 Pascal Works with: Free Pascal Optimized for speed, by using the state before in IncSumDigit. program Niven; const base = 10; type tNum = longword;{Uint64} const cntbasedigits = trunc(ln(High(tNum))/ln(base))+1; type tSumDigit = record sdNumber : tNum; sdDigits : array[0..cntbasedigits-1] of byte; sdSumDig : byte; sdIsNiven : boolean; end; function InitSumDigit( n : tNum):tSumDigit; var sd : tSumDigit; qt : tNum; i : integer; begin with sd do begin sdNumber:= n; fillchar(sdDigits,SizeOf(sdDigits),#0); sdSumDig :=0; sdIsNiven := false; i := 0; // calculate Digits und sum them up while n > 0 do begin qt := n div base; {n mod base} sdDigits[i] := n-qt*base; inc(sdSumDig,sdDigits[i]); n:= qt; inc(i); end; IF sdSumDig >0 then sdIsNiven := (sdNumber MOD sdSumDig = 0); end; InitSumDigit:=sd; end; procedure IncSumDigit(var sd:tSumDigit); var i,d: integer; begin i := 0; with sd do begin inc(sdNumber); repeat d := sdDigits[i]; inc(d); inc(sdSumDig); //base-1 times the repeat is left here if d < base then begin sdDigits[i] := d; BREAK; end else begin sdDigits[i] := 0; dec(sdSumDig,base); inc(i); end; until i > high( sdDigits); sdIsNiven := (sdNumber MOD sdSumDig) = 0; end; end; var MySumDig : tSumDigit; ln : tNum; cnt: integer; begin MySumDig:=InitSumDigit(0); cnt := 0; repeat IncSumDigit(MySumDig); IF MySumDig.sdIsNiven then begin write(MySumDig.sdNumber,'.'); inc(cnt); end; until cnt >= 20; write('....'); MySumDig:=InitSumDigit(1000); repeat IncSumDigit(MySumDig); until MySumDig.sdIsNiven; writeln(MySumDig.sdNumber,'.'); // searching for big gaps between two niven-numbers // MySumDig:=InitSumDigit(18879989100-276); MySumDig:=InitSumDigit(1); cnt := 0; ln:= MySumDig.sdNumber; repeat IncSumDigit(MySumDig); if MySumDig.sdIsNiven then begin IF cnt < (MySumDig.sdNumber-ln) then begin cnt :=(MySumDig.sdNumber-ln); writeln(ln,' --> ',MySumDig.sdNumber,' d=',cnt); end; ln:= MySumDig.sdNumber; end; until MySumDig.sdNumber= High(tNum); { 689988915 --> 689989050 d=135 879987906 --> 879988050 d=144 989888823 --> 989888973 d=150 2998895823 --> 2998895976 d=153 ~ 24 Cpu-cycles per test i3- 4330 1..2^32-1} end. output: 1.2.3.4.5.6.7.8.9.10.12.18.20.21.24.27.30.36.40.42.....1002. Perl #!/usr/bin/perl use strict ; use warnings ; use List::Util qw ( sum ) ; sub createHarshads { my @harshads ; my$number = 1 ;
do {
if ( $number % sum ( split ( // ,$number ) ) == 0 ) {
push @harshads , $number ; }$number++ ;
} until ( $harshads[ -1 ] > 1000 ) ; return @harshads ; } my @harshadnumbers = createHarshads ; for my$i ( 0..19 ) {
print "$harshadnumbers[$i ]\n" ;
}
print "The first Harshad number greater than 1000 is $harshadnumbers[ -1 ]!\n" ; Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 The first Harshad number greater than 1000 is 1002! Perl 6 Works with: Rakudo version 2016.08 constant @harshad = grep {$_ %% .comb.sum }, 1 .. *;

Output:
(1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42)
1002

Phix

integer n = 0
sequence digits={0}

procedure nNiven()
while 1 do
n += 1
for i=length(digits) to 0 by -1 do
if i=0 then
digits = prepend(digits,1)
exit
end if
if digits[i]<9 then
digits[i] += 1
exit
end if
digits[i] = 0
end for
if remainder(n,sum(digits))=0 then exit end if
end while
end procedure

sequence s = {}
for i=1 to 20 do
nNiven()
s &= n
end for
?s
while n<=1000 do
nNiven()
end while
?n
Output:
{1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42}
1002

Alternative version

return remainder(n,sum(sq_sub(sprint(n),'0')))=0
end function

sequence s = {}
integer n = 0
while length(s)<20 do
n += 1
s &= n
end if
end while
n = 1001
while not isHarshad(n) do n += 1 end while
?s&n
Output:
{1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42,1002}

PicoLisp

#if niven number, return it.
(de niven (N)
(if (=0 (% N (apply+ (getN N)))) N) )

#function which creates a list of numbers from input
(de getN (N)
(mapcar any (chop N)) )

#function to apply '+' func to list of numbers
(de apply+ (Ln)
(apply + Ln) )

#function to delete NIL from the entire list
(de delNIL (L)
(delete NIL L T) )

#This function generates niven number list
(de nivGen (R N)
(delNIL (mapcar niven (range R N))) )

#print 1st 20 niven numbers and 1st niven number greater than 1000
(nivGen 1 1000) ) ~(head 1 (nivGen 1001 1010)) ) )

Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002

PL/I

*process source or(!) xref attributes;
niven: Proc Options(main);
/*********************************************************************
* 08-06.2013 Walter Pachl translated from Rexx
* with a slight improvement: Do j=y+1 By 1;
*********************************************************************/

Dcl SYSPRINT Print;

Dcl (x,y) dec fixed(8);
x=20;
y=1000;
Begin;
Dcl (n(x),j) Dec Fixed(8);
Dcl ni Bin Fixed(31) Init(0);
Dcl result Char(100) Var Init('');
loop:
Do j=1 By 1;
If mod(j,sumdigs(j))=0 Then Do;
ni+=1;
n(ni)=j;
result=result!!' '!!d2c(j);
If ni=x Then Leave loop;
End;
End;
Put Edit('first 20 Niven numbers: ',result)(Skip,a,a);
Do j=y+1 By 1;
If mod(j,sumdigs(j))=0 Then
Leave;
End;
Put Edit('first Niven number > ',d2c(y),' is: ',d2c(j))(Skip,4(a));
End;

sumDigs: proc(z) Returns(Dec Fixed(3));
Dcl z Pic'(8)9';
Dcl i Bin Fixed(31);
Dcl sd Dec Fixed(3) Init(0);
Do i=1 To hbound(d);
sd+=d(i);
End;
Return(sd);
End;

d2c: Proc(z) Returns(char(8) Var);
Dcl z Pic'(8)z';
Dcl p Bin Fixed(31);
p=verify(z,' ');
Return(substr(z,p));
End;

End;
Output:
first 20 Niven numbers:  1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42
first Niven number > 1000 is: 1002

PowerShell

Works with: PowerShell version 2

In PowerShell, we generally don't wrap every little thing in a function. If you have something simple to do, you just do it.

1..1000 | Where { $_ % ( [int[]][string[]][char[]][string]$_ | Measure -Sum ).Sum -eq 0 } | Select -First 20
1001..2000 | Where { $_ % ( [int[]][string[]][char[]][string]$_ | Measure -Sum ).Sum -eq 0 } | Select -First 1

Output:
1
2
3
4
5
6
7
8
9
10
12
18
20
21
24
27
30
36
40
42
1002

But if we do have a need for the code to be reusable, we can do that.

{
<#
.SYNOPSIS
Returns numbers in the Harshad or Niven series.

.DESCRIPTION
Returns all integers in the given range that are evenly divisible by the sum of their digits
in ascending order.

.PARAMETER Minimum
Lower bound of the range to search for Harshad numbers. Defaults to 1.

.PARAMETER Maximum
Upper bound of the range to search for Harshad numbers. Defaults to 2,147,483,647

.PARAMETER Count
Maximum number of Harshad numbers to return.
#>

[cmdletbinding()]
Param (
[int]$Minimum = 1, [int]$Maximum = [int]::MaxValue,
[int]$Count ) # Skip any non-positive numbers in the specified range$Minimum = [math]::Max( 1, $Minimum ) # If the adjusted range has any numbers in it... If ($Maximum -ge $Minimum ) { # If a count was specified, build a parameter for the Select statement to kill the pipeline when the count is achieved. If ($Count ) { $SelectParam = @{ First =$Count } }
Else { $SelectParam = @{} } # For each number in the range, test the remainder of it divided it by iteself (converted to a string, # then a character array, then a string array, then an integer array, then summed).$Minimum..$Maximum | Where {$_ % ( [int[]][string[]][char[]][string]$_ | Measure -Sum ).Sum -eq 0 } | Select @SelectParam } } Get-HarshadNumbers -Count 20 Get-HarshadNumbers -Minimum 1001 -Count 1 Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 Prolog Works with SWI-Prolog and module lambda.pl written by Ulrich Neumerkel, it can be found there : http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl. :- use_module(library(lambda)). niven :- nb_setval(go, 1), L = [1 | _], print_niven(L, 1), gen_niven(1, L). print_niven([X|T], N) :- when(ground(X), ( ( nb_getval(go, 1) -> ( N < 20 -> writeln(X), N1 is N+1, print_niven(T, N1) ; ( X > 1000 -> writeln(X), nb_setval(go, 0) ; N1 is N+1, print_niven(T, N1))) ; true))). gen_niven(X, [N | T]) :- ( nb_getval(go, 1) -> X1 is X+1, sum_of_digit(X, S), ( X mod S =:= 0 -> N = X, gen_niven(X1, T) ; gen_niven(X1, [N | T])) ; true). sum_of_digit(N, S) :- number_chars(N, LC), maplist(\X^Y^number_chars(Y, [X]), LC, LN), sum_list(LN, S). Output: ?- niven. 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 1002 true. Python >>> import itertools >>> def harshad(): for n in itertools.count(1): if n % sum(int(ch) for ch in str(n)) == 0: yield n >>> list(itertools.islice(harshad(), 0, 20)) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42] >>> for n in harshad(): if n > 1000: print(n) break 1002 >>> Python: Functional The for loop above could be changed to the following to find the number > 1000; in fact the harshad generator function could become a generator expression creating this more functional version: >>> from itertools import count, islice >>> harshad = (n for n in count(1) if n % sum(int(ch) for ch in str(n)) == 0) >>> list(islice(harshad, 0, 20)) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42] >>> next(x for x in harshad if x > 1000) 1002 >>> Racket #lang racket (define (digsum n) (for/sum ([c (number->string n)]) (string->number [string c]))) (define harshads (stream-filter (λ (n) (= (modulo n (digsum n)) 0)) (in-naturals 1))) ; First 20 harshad numbers (displayln (for/list ([i 20]) (stream-ref harshads i))) ; First harshad greater than 1000 (displayln (for/first ([h harshads] #:when(> h 1000)) h)) Output: (1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42) 1002 Different to the Scheme implementation in that it illustrates Racket's native iterators, and let-values with quotient/remainder: #lang racket (require math/number-theory) (define (digital-sum n) (let inner ((n n) (s 0)) (if (zero? n) s (let-values ([(q r) (quotient/remainder n 10)]) (inner q (+ s r)))))) (define (harshad-number? n) (and (>= n 1) (divides? (digital-sum n) n))) ;; find 1st 20 Harshad numbers (for ((i (in-range 1 (add1 20))) (h (sequence-filter harshad-number? (in-naturals 1)))) (printf "#~a ~a~%" i h)) ;; find 1st Harshad number > 1000 (displayln (for/first ((h (sequence-filter harshad-number? (in-naturals 1001)))) h)) Output: #1 1 #2 2 #3 3 #4 4 #5 5 #6 6 #7 7 #8 8 #9 9 #10 10 #11 12 #12 18 #13 20 #14 21 #15 24 #16 27 #17 30 #18 36 #19 40 #20 42 1002 REXX These REXX examples allow the user to specify how many Niven numbers to list, as well as find the first Niven number greater than a specified positive integer. Also, gihugeic integers are supported (essentially no limit). generic /*REXX program finds the first A Niven numbers; it also finds first Niven number > B.*/ parse arg A B . /*obtain optional arguments from the CL*/ if A=='' | A==',' then A= 20 /*Not specified? Then use the default.*/ if B=='' | B==',' then B=1000 /* " " " " " " */ numeric digits 1+max(8, length(A), length(B)) /*enable the use of any sized numbers. */ #=0;$= /*set Niven numbers count; Niven list.*/
do j=1 until #==A /*◄───── let's go Niven number hunting.*/
if j//sumDigs(j)==0 then do; #=#+1; $=$ j; end
end /*j*/ /* [↑] bump count; append J ──► list.*/

say 'first' A 'Niven numbers:' $do t=B+1 until t//sumDigs(t)==0; end /*hunt for a Niven (or Harshad) number.*/ say 'first Niven number >' B " is: " t exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sumDigs: procedure; parse arg x; s=0; do k=1 for length(x); s=s+substr(x,k,1); end /*k*/ output when using the default inputs: first 20 Niven numbers: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 first Niven number > 1000 is: 1002 idomatic This REXX version idiomatically uses a isNiven function. /*REXX program finds the first A Niven numbers; it also finds first Niven number > B.*/ parse arg A B . /*obtain optional arguments from the CL*/ if A=='' | A==',' then A= 20 /*Not specified? Then use the default.*/ if B=='' | B==',' then B=1000 /* " " " " " " */ numeric digits 1+max(8, length(A), length(B)) /*enable the use of any sized numbers. */ #=0;$= /*set Niven numbers count; Niven list.*/
do j=1 until #==A /*◄───── let's go Niven number hunting.*/
if isNiven(j) then do; #=#+1; $=$ j; end
end /*j*/ /* [↑] bump count; append J ──► list.*/

say 'first' A 'Niven numbers:' $do t=B+1 until isNiven(t); end /*hunt for a Niven (or Harshad) number.*/ say 'first Niven number >' B " is: " t exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ isNiven: procedure; parse arg x; s=0; do k=1 for length(x); s=s+substr(x,k,1); end /*k*/ return x//s==0 output is identical to the 1st REXX version. esoteric This REXX version optimizes the isNiven function by using parse statements instead of the substr BIF, yielding a faster algorithm. /*REXX program finds the first A Niven numbers; it also finds first Niven number > B.*/ parse arg A B . /*obtain optional arguments from the CL*/ if A=='' | A==',' then A= 20 /*Not specified? Then use the default.*/ if B=='' | B==',' then B=1000 /* " " " " " " */ numeric digits 1+max(8, length(A), length(B)) /*enable the use of any sized numbers. */ #=0;$= /*set Niven numbers count; Niven list.*/
do j=1 until #==A /*◄───── let's go Niven number hunting.*/
if isNiven(j) then do; #=#+1; $=$ j; end
end /*j*/ /* [↑] bump count; append J ──► list.*/

say 'first' A 'Niven numbers:' $do t=B+1 until isNiven(t); end /*hunt for a Niven (or Harshad) number.*/ say 'first Niven number >' B " is: " t exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ isNiven: procedure; parse arg x 1 sum 2 q /*use the first decimal digit for SUM.*/ do while q\==''; parse var q _ 2 q; sum=sum+_; end /*k*/ /* ↑ */ return x//sum==0 /* └───◄ is destructively parsed. */ output is identical to the 1st REXX version. array of numbers This REXX version builds an array of numbers instead of a list (building an array is much faster than building a list, especially if the list is very long). In addition, if the A number is negative, the numbers in the array aren't displayed, but the last number in the array is displayed. /*REXX program finds the first A Niven numbers; it also finds first Niven number > B.*/ parse arg A B . /*obtain optional arguments from the CL*/ if A=='' | A==',' then A= 20 /*Not specified? Then use the default.*/ if B=='' | B==',' then B=1000 /* " " " " " " */ tell= A>0; A=abs(A) /*flag for showing a Niven numbers list*/ A=abs(a) numeric digits 1+max(8, length(A), length(B)) /*enable the use of any sized numbers. */ #=0;$= /*set Niven numbers count; Niven list.*/
do j=1 until #==A /*◄───── let's go Niven number hunting.*/
if isNiven(j) then do; #=#+1;  !.#=j; end
end /*j*/ /* [↑] bump count; append J ──► list.*/
w=length(!.w) /*W: is the width of largest Niven #.*/
if tell then do
say 'first' A 'Niven numbers:'; do k=1 for #; say right(!.k, w); end /*k*/
end
else say 'last of the' A 'Niven numbers: '  !.#
say
do t=B+1 until isNiven(t); end /*hunt for a Niven (or Harshad) number.*/

say 'first Niven number >' B " is: " t
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isNiven: procedure; parse arg x 1 sum 2 q /*use the first decimal digit for SUM.*/
do while q\==''; parse var q _ 2 q; sum=sum+_; end /*k*/
/* ↑ */
return x//sum==0 /* └───◄ is destructively parsed. */

output   when the input used is:   -1000000   66777888

last of the 1000000 Niven numbers:  12150510

first Niven number > 66777888  is:  66777900

Ring

i = 1
count = 0
while true
sum = 0
if niven(i) = 1
if count < 20 see "" + i + " is a Niven number" + nl count +=1 ok
if i > 1000 see "" + i + " is a Niven number" exit ok ok
i + =1
end

func niven nr
nrString = string(nr)
for j = 1 to len(nrString)
sum = sum + number(nrString[j])
next
niv = ((nr % sum) = 0)
return niv

Output:

1 is a Niven number
2 is a Niven number
3 is a Niven number
4 is a Niven number
5 is a Niven number
6 is a Niven number
7 is a Niven number
8 is a Niven number
9 is a Niven number
10 is a Niven number
12 is a Niven number
18 is a Niven number
20 is a Niven number
21 is a Niven number
24 is a Niven number
27 is a Niven number
30 is a Niven number
36 is a Niven number
40 is a Niven number
42 is a Niven number
1002 is a Niven number

Ruby

Works with: Ruby version 2.4

Ruby 2.4 gave Integers a digits method, and Arrays a sum method.

harshad = 1.step.lazy.select { |n| n % n.digits.sum == 0 }

p harshad.find { |n| n > 1000 }
Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42]
1002

Run BASIC

while count < 20
h = h + 1
if neven(h) = 0 then
count = count + 1
print count;": ";h
end if
wend

h = 1000
while 1 = 1
h = h + 1
if neven(h) = 0 then
print h
exit while
end if
wend

function neven(h)
h$= str$(h)
for i = 1 to len(h$) d = d + val(mid$(h$,i,1)) next i neven = h mod d end function Output: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 11: 12 12: 18 13: 20 14: 21 15: 24 16: 27 17: 30 18: 36 19: 40 20: 42 1002 Rust fn is_hashard (n : u32) -> bool { let sum_digits = n.to_string() .chars() .map(|c| c.to_digit(10).unwrap()) .fold(0, |a, b| a+b); n % sum_digits == 0 } fn main() { for i in (1u32..).filter(|num| is_hashard(*num)).take(20) { println!("Hashard : {}", i); } for i in (1_001u32..).filter(|num| is_hashard(*num)).take(1) { println!("First Hashard bigger than 1_000 : {}", i); } } Output: Hashard : 1 Hashard : 2 Hashard : 3 Hashard : 4 Hashard : 5 Hashard : 6 Hashard : 7 Hashard : 8 Hashard : 9 Hashard : 10 Hashard : 12 Hashard : 18 Hashard : 20 Hashard : 21 Hashard : 24 Hashard : 27 Hashard : 30 Hashard : 36 Hashard : 40 Hashard : 42 First Hashard bigger than 1_000 : 1002 Scala object Harshad extends App { val harshads = Stream from 1 filter (i => i % i.toString.map(_.asDigit).sum == 0) println(harshads.take(20).toList) println(harshads.filter(_ > 1000).head) } Output: List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42) 1002 Scheme #!/usr/local/bin/gosh ;; Show the first 20 niven numbers and the ;; first one greater than 1000. (define (main args) (display (iota-filtered 20 1 niven?))(newline) (display (iota-filtered 1 1001 niven?))(newline)) ;; Return a list of length n ;; for numbers starting at start ;; that satisfy the predicate fn. (define (iota-filtered n start fn) (let loop ((num start)(lst (list))) (if (= (length lst) n) lst (loop (+ 1 num) (if (fn num) (append lst (list num)) lst))))) ;; Is a number a niven number? (define (niven? n) (and (> n 0) (= 0 (remainder n (sum-of-digits n))))) ;; Get the sum of the digits of a number. (define (sum-of-digits n) (apply + (map string->number (map string (string->list (number->string n)))))) Output: (1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42) (1002) Seed7$ include "seed7_05.s7i";

const func integer: sumOfDigits (in var integer: num) is func
result
var integer: sum is 0;
begin
repeat
sum +:= num rem 10;
num := num div 10;
until num = 0;
end func;

const func integer: nextHarshadNum (inout integer: num) is func
result
begin
while num mod sumOfDigits(num) <> 0 do
incr(num);
end while;
end func;

const proc: main is func
local
var integer: current is 1;
var integer: count is 0;
begin
for count range 1 to 20 do
incr(current);
end for;
current := 1001;
end func;
Output:
1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42  ... 1002

Sidef

var n = 0;
{
++n while !(n %% n.digits.sum);
n;
}
}

say 20.of { iter.run };

var n;
do {
n = iter.run
} while (n <= 1000);

say n;
Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42]
1002

Sinclair ZX81 BASIC

Works with 1k of RAM. FAST isn't all that fast.

10 FAST
20 LET N=0
30 LET H=0
40 LET N=N+1
50 LET N$=STR$ N
60 LET SD=0
70 FOR I=1 TO LEN N$80 LET SD=SD+VAL N$(I)
90 NEXT I
100 IF N/SD<>INT (N/SD) THEN GOTO 40
110 LET H=H+1
120 IF H<=20 OR N>1000 THEN PRINT N
130 IF N>1000 THEN GOTO 150
140 GOTO 40
150 SLOW
Output:
1
2
3
4
5
6
7
8
9
10
12
18
20
21
24
27
30
36
40
42
1002

Tcl

# Determine if the given number is a member of the class of Harshad numbers
if {$n < 1} {return false} set sum [tcl::mathop::+ {*}[split$n ""]]
return [expr {$n%$sum == 0}]
}

# Get the first 20 numbers that satisfy the condition
for {set n 1; set harshads {}} {[llength $harshads] < 20} {incr n} { if {[isHarshad$n]} {
lappend harshads $n } } puts [format "First twenty Harshads: %s" [join$harshads ", "]]

# Get the first value greater than 1000 that satisfies the condition
for {set n 1000} {![isHarshad [incr n]]} {} {}
puts "First Harshad > 1000 = $n" Output: First twenty Harshads: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42 First Harshad > 1000 = 1002 uBasic/4tH C=0 For I = 1 Step 1 Until C = 20 ' First 20 Harshad numbers If FUNC(_FNHarshad(I)) Then Print I;" "; : C = C + 1 Next For I = 1001 Step 1 ' First Harshad greater than 1000 If FUNC(_FNHarshad(I)) Then Print I;" " : Break Next End _FNHarshad Param(1) Local(2) [email protected] = [email protected] [email protected] = 0 Do While ([email protected] > 0) [email protected] = [email protected] + ([email protected] % 10) [email protected] = [email protected] / 10 Loop Return (([email protected] % [email protected]) = 0) Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 0 OK, 0:185 VBA Option Explicit Sub Main() Dim i As Long, out As String, Count As Integer Do i = i + 1 If IsHarshad(i) Then out = out & i & ", ": Count = Count + 1 Loop While Count < 20 Debug.Print "First twenty Harshad numbers are : " & vbCrLf & out & "..." i = 1000 Do i = i + 1 Loop While Not IsHarshad(i) Debug.Print "The first harshad number after 1000 is : " & i End Sub Function IsHarshad(sNumber As Long) As Boolean Dim Summ As Long, i As Long, temp temp = Split(StrConv(sNumber, vbUnicode), Chr(0)) For i = LBound(temp) To UBound(temp) - 1 Summ = Summ + temp(i) Next i IsHarshad = sNumber Mod Summ = 0 End Function Output: First twenty Harshad numbers are : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, ... The first harshad number after 1000 is : 1002 VBScript n = 0 m = 1 first20 = "" after1k = "" Do If IsHarshad(m) And n <= 20 Then first20 = first20 & m & ", " n = n + 1 m = m + 1 ElseIf IsHarshad(m) And m > 1000 Then after1k = m Exit Do Else m = m + 1 End If Loop WScript.StdOut.Write "First twenty Harshad numbers are: " WScript.StdOut.WriteLine WScript.StdOut.Write first20 WScript.StdOut.WriteLine WScript.StdOut.Write "The first Harshad number after 1000 is: " WScript.StdOut.WriteLine WScript.StdOut.Write after1k Function IsHarshad(s) IsHarshad = False sum = 0 For i = 1 To Len(s) sum = sum + CInt(Mid(s,i,1)) Next If s Mod sum = 0 Then IsHarshad = True End If End Function Output: First twenty Harshad numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, The first Harshad number after 1000 is: 1002 Visual FoxPro LOCAL lnCount As Integer, k As Integer CLEAR lnCount = 0 k = 0 *!* First 20 numbers ? "First 20 numbers:" DO WHILE lnCount < 20 k = k + 1 IF Harshad(k) lnCount = lnCount + 1 ? lnCount, k ENDIF ENDDO *!* First such number > 1000 k = 1001 DO WHILE NOT Harshad(k) k = k + 1 ENDDO ? "First such number > 1000", k FUNCTION Harshad(n As Integer) As Boolean LOCAL cn As String, d As Integer, i As Integer cn = TRANSFORM(n) d = 0 FOR i = 1 TO LEN(cn) d = d + VAL(SUBSTR(cn, i, 1)) ENDFOR RETURN n % d = 0 ENDFUNC Output: First 20 numbers: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 12 12 18 13 20 14 21 15 24 16 27 17 30 18 36 19 40 20 42 First such number > 1000: 1002 Whitespace </lang> This solution was generated from the pseudo-Assembly below. A live run is available for the inquiring skeptic. push 0 ; Harshad numbers found push 0 ; counter 0: ; Increment the counter, call "digsum", branch on the modulus. push 1 add dup dup push 0 call 1 mod jz 2 jump 0 1: ; [n 0] => [digsum(n)] copy 1 push 10 mod add swap push 10 div swap push 0 copy 2 sub jn 1 slide 1 ret 2: ; Should we print this Harshad number? push 1000 copy 1 sub jn 3 ; We're done if it's greater than 1000. swap push 1 add swap ; Increment how many we've found so far. push 20 copy 2 sub jn 0 ; If we've already got 20, go back to the top. dup onum push 32 ochr ; Otherwise, print it and a space. jump 0 ; And /then/ go back to the top. 3: ; Print the > 1000 Harshad number on its own line and exit clean. push 10 ochr onum pop push 10 ochr exit Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 XPL0 include c:\cxpl\codes; \intrinsic 'code' declarations int H, C, N, S; \Harshad number, Counter, Number, Sum [H:= 1; C:= 0; loop [N:= H; S:= 0; \sum digits repeat N:= N/10; S:= S + rem(0); until N = 0; if rem(H/S) = 0 then \Harshad no.is evenly divisible by sum of digits [if C < 20 then [IntOut(0, H); ChOut(0, ^ ); C:= C+1]; if H > 1000 then [IntOut(0, H); CrLf(0); quit]; ]; H:= H+1; ]; ] Output: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 1002 zkl fcn harshad(n){ 0==n%(n.split().sum(0)) } [1..].tweak(fcn(n){ if(not harshad(n)) return(Void.Skip); n }) .walk(20).println(); [1..].filter(20,harshad).println(); [1001..].filter1(harshad).println(); Walkers are zkl iterators. [a..b] is a Walker from a to b. Walkers can be tweaked to transform the sequence they are walking. In this case, ignore non Harshad numbers. Then tell the walker to get 20 items from that [modified] sequence. In this case, filters are the better solution. Output: L(1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42) L(1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42) L(1002) ZX Spectrum Basic Translation of: AWK 10 LET k=0: LET n=0 20 IF k=20 THEN GO TO 60 30 LET n=n+1: GO SUB 1000 40 IF isHarshad THEN PRINT n;" ";: LET k=k+1 50 GO TO 20 60 LET n=1001 70 GO SUB 1000: IF NOT isHarshad THEN LET n=n+1: GO TO 70 80 PRINT '"First Harshad number larger than 1000 is ";n 90 STOP 1000 REM is Harshad? 1010 LET s=0: LET n$=STR$n 1020 FOR i=1 TO LEN n$
1030 LET s=s+VAL n\$(i)
1040 NEXT i