Special divisors
- Task
Numbers n such that reverse(d) divides reverse(n) for all divisors d of n, where n < 200
Julia
<lang julia>using Primes
function divisors(n)
f = [one(n)]
for (p,e) in factor(n)
f = reduce(vcat, [f*p^j for j in 1:e], init=f)
end
return f[1:end-1]
end
function isspecialdivisor(n)::Bool
isprime(n) && return true
nreverse = evalpoly(10, reverse(digits(n)))
for d in divisors(n)
dreverse = evalpoly(10, reverse(digits(d)))
!(nreverse ÷ dreverse ≈ nreverse / dreverse) && return false
end
return true
end
const specials = filter(isspecialdivisor, 1:200) foreach(p -> print(rpad(p[2], 4), p[1] % 18 == 0 ? "\n" : ""), enumerate(specials))
</lang>
- Output:
1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Perl
<lang perl>use strict; use warnings; use feature 'say'; use ntheory 'divisors';
my @sd; for my $n (1..199) {
sub rev { join , reverse split , shift }
map { next if $_ != int $_ } map { rev($n) / rev $_ } divisors $n;
push @sd, $n;
}
say scalar(@sd) . " matching numbers:\n" .
(sprintf "@{['%4d' x @sd]}", @sd) =~ s/(.{40})/$1\n/gr;</lang>
- Output:
72 matching numbers: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Phix
function rev(integer n) integer r = 0 while n do r = r*10+remainder(n,10) n = floor(n/10) end while return r end function function special_divisors(integer n) sequence fn = factors(n) if length(fn) then integer rn = rev(n) for i=1 to length(fn) do if remainder(rn,rev(fn[i])) then return false end if end for end if return true end function sequence res = apply(true,sprintf,{{"%3d"},filter(tagset(200),special_divisors)}) printf(1,"Found %d special divisors:\n%s\n",{length(res),join_by(res,1,18)})
- Output:
Found 72 special divisors: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
Raku
<lang perl6>use Prime::Factor:ver<0.3.0+>;
say "{+$_} matching numbers:\n{.batch(10)».fmt('%3d').join: "\n"}"
given (1..^200).grep: { all .flip «%%« .&divisors».flip };</lang>
- Output:
72 matching numbers: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199
REXX
<lang rexx>/*REXX program finds special divisors: numbers N such that reverse(D) divides */ /*───────────────────────────────────────────── reverse(N) for all divisors D of N. */ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 200 /* " " " " " " */ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= 10 /*width of a number in any column. */
@sdns= ' special divisors N that reverse(D) divides reverse(N)' ,
'for all divisors D of N, where N < ' commas(hi)
if cols>0 then say ' index │'center(@sdns, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') sdns= 0; idx= 1 /*initialize # of nice primes and index*/ $= /*a list of nice primes (so far). */
do j=1 for hi-1; r= reverse(j) /*search for special divisors. */
do k=2 to j%2 /*skip the first divisor (unity) & last*/
if j//k==0 then if r//reverse(k)==0 then nop /*Is OK? keep*/
else iterate j /*Not OK? Skip*/
end /*m*/
sdns= sdns + 1 /*bump the number of sdns numbers. */
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(j) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a nice prime ──► list, allow big#*/
if sdns//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ say say 'Found ' commas(sdns) @sdns exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>
- output when using the default inputs:
index │ special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 1 2 3 4 5 6 7 8 9 11 11 │ 13 17 19 22 23 26 27 29 31 33 21 │ 37 39 41 43 44 46 47 53 55 59 31 │ 61 62 66 67 69 71 73 77 79 82 41 │ 83 86 88 89 93 97 99 101 103 107 51 │ 109 113 121 127 131 137 139 143 149 151 61 │ 157 163 167 169 173 179 181 187 191 193 71 │ 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl
row = 0 num = 0 limit1 = 200
for n = 1 to limit1
flag = 1
revNum = rever(string(n))
revNum = number(revNum)
for m = 1 to n/2
revDiv = rever(String(m))
revDiv = number(revDiv)
if n%m = 0
if revNum % revDiv = 0
flag = 1
else
flag = 0
exit
ok
ok
next
if flag = 1
num = num + 1
row = row + 1
see "" + n + " "
if row%10 = 0
see nl
ok
ok
next
see nl + "Found " + num + " special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200" + nl see "done..." + nl
func rever(str)
rev = ""
for n = len(str) to 1 step -1
rev = rev + str[n]
next
return rev
</lang>
- Output:
working... 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 Found 72 special divisors N that reverse(D) divides reverse(N) for all divisors D of N, where N < 200 done...
Wren
<lang ecmascript>import "/math" for Int import "/seq" for Lst import "/fmt" for Fmt
var reversed = Fn.new { |n|
var rev = 0
while (n > 0) {
rev = rev * 10 + n % 10
n = (n/10).floor
}
return rev
}
var special = [] for (n in 1...200) {
var divs = Int.divisors(n)
var revN = reversed.call(n)
if (divs.all { |d| revN % reversed.call(d) == 0 }) special.add(n)
} System.print("Special divisors in the range 0..199:") for (chunk in Lst.chunks(special, 12)) Fmt.print("$3d", chunk) System.print("\n%(special.count) special divisors found.")</lang>
- Output:
Special divisors in the range 0..199: 1 2 3 4 5 6 7 8 9 11 13 17 19 22 23 26 27 29 31 33 37 39 41 43 44 46 47 53 55 59 61 62 66 67 69 71 73 77 79 82 83 86 88 89 93 97 99 101 103 107 109 113 121 127 131 137 139 143 149 151 157 163 167 169 173 179 181 187 191 193 197 199 72 special divisors found.