Idoneal numbers: Difference between revisions
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{{
'''[[wp:Idoneal_number|Idoneal numbers]]''' (also called '''suitable''' numbers or '''convenient''' numbers) are the positive integers '''D''' such that any integer expressible in only one way as '''x<sup>2</sup> ± Dy<sup>2</sup>''' (where '''x<sup>2</sup>''' is relatively prime to '''Dy<sup>2</sup>''') is a prime power or twice a prime power.
Line 19:
;* [[wp:Idoneal_number|Wikipedia: Idoneal numbers]]
;* [[oeis:A000926|OEIS:A000926 - Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers)]]
;* [[O'Halloran numbers]]
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">
F is_idoneal(num)
‘ Return true if num is an idoneal number ’
L(a) 1 .< num
L(b) a + 1 .< num
I a * b + a + b > num
L.break
L(c) b + 1 .< num
V sum3 = a * b + b * c + a * c
I sum3 == num
R 0B
I sum3 > num
L.break
R 1B
V row = 0
L(n) 1..1999
I is_idoneal(n)
row++
print(f:‘{n:5}’, end' I row % 13 == 0 {"\n"} E ‘’)
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|ABC}}==
<syntaxhighlight lang="abc">
HOW TO RETURN a over b: RETURN floor( a / b )
HOW TO REPORT is.idoneal n:
PUT 1 IN idoneal
PUT 0 IN a
PUT n over 2 IN max.a
WHILE idoneal = 1 AND a < max.a:
PUT a + 1 IN a
PUT a IN b
PUT n IN c
PUT 0 IN sum
PUT 1 IN again
WHILE b < c AND b < n - 1 AND sum <= n AND idoneal = 1:
PUT b + 1 IN b
PUT a * b IN ab
PUT ( n - ab ) over ( a + b ) IN c
PUT ab + ( c * ( b + a ) ) IN sum
IF c > b AND sum = n:
PUT 0 IN idoneal
REPORT idoneal = 1
PUT 0 IN count
PUT 0 IN n
WHILE count < 65:
PUT n + 1 IN n
IF is.idoneal n:
WRITE n >> 5
PUT count + 1 IN count
IF count mod 13 = 0: WRITE /
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|Action!}}==
<syntaxhighlight lang="action!">
;;; find idoneal numbers - numbers that cannot be written as ab + bc + ac
;;; where 0 < a < b < c
;;; there are 65 known idoneal numbers
PROC Main()
CARD count, maxCount, n, a, b, c, ab, sum
BYTE idoneal
count = 0 maxCount = 65
n = 0
WHILE count < maxCount DO
n ==+ 1
idoneal = 1
a = 1
WHILE ( a + 2 ) < n AND idoneal = 1 DO
b = a + 1
DO
ab = a * b
sum = 0
IF ab < n THEN
c = ( n - ab ) / ( a + b )
sum = ab + ( c * ( b + a ) )
IF c > b AND sum = n THEN idoneal = 0 FI
b ==+ 1
FI
UNTIL sum > n OR idoneal = 0 OR ab >= n
OD
a ==+ 1
OD
IF idoneal THEN
Put(' )
IF n < 10 THEN Put(' ) FI
IF n < 100 THEN Put(' ) FI
IF n < 1000 THEN Put(' ) FI
PrintC( n )
count ==+ 1
IF count MOD 13 = 0 THEN PutE() FI
FI
OD
RETURN
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|ALGOL 68}}==
Note, AND does not shortcut in Algol 68.
<syntaxhighlight lang="algol68">
BEGIN # find idoneal numbers - numbers that cannot be written as ab + bc + ac #
# where 0 < a < b < c #
# there are 65 known idoneal numbers #
INT count := 0;
INT max count = 65;
FOR n WHILE count < max count DO
BOOL idoneal := TRUE;
FOR a TO n OVER 2 WHILE idoneal DO
FOR b FROM a + 1 TO n - 1
WHILE INT ab = a * b;
INT c = ( n - ab ) OVER ( a + b );
INT sum = ab + ( c * ( b + a ) );
sum <= n
AND b < c
AND ( idoneal := c <= b OR sum /= n )
DO SKIP OD
OD;
IF idoneal THEN
print( ( " ", whole( n, -4 ) ) );
IF ( count +:= 1 ) MOD 13 = 0 THEN print( ( newline ) ) FI
FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">
begin % find idoneal numbers - numbers that cannot be written as ab + bc + ac %
% where 0 < a < b < c %
% there are 65 known idoneal numbers %
integer count, MAX_COUNT, n;
MAX_COUNT := 65;
count := 0;
n := 0;
while count < MAX_COUNT do begin
logical idoneal;
integer a;
n := n + 1;
idoneal := true;
a := 1;
while ( a + 2 ) < n and idoneal do begin
integer b;
b := a + 1;
while begin
integer ab, sum;
ab := a * b;
sum := 0;
if ab < n then begin
integer c;
c := ( n - ab ) div ( a + b );
sum := ab + ( c * ( b + a ) );
if c > b and sum = n then idoneal := false;
b := b + 1
end if_ab_lt_n ;
sum <= n and idoneal and ab < n
end do begin end;
a := a + 1
end;
if idoneal then begin
count := count + 1;
writeon( i_w := 4, s_w := 0, " ", n );
if count rem 13 = 0 then write()
end if_idoneal
end while_count_lt_MAX_COUNT
end.
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">idoneal?: function [n][
loop 1..n 'a [
loop (a+1)..n 'b [
if n < a*b + a + b -> break
loop (b+1)..n 'c [
s: sum @[a*b b*c a*c]
if s = n -> return false
if s > n -> break
]
]
]
return true
]
idoneals: select 1..1850 => idoneal?
loop split.every: 13 idoneals 'x ->
print map x 's -> pad to :string s 4</syntaxhighlight>
{{out}}
<pre> 1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848</pre>
=={{header|BASIC}}==
Line 51 ⟶ 296:
<pre>Same as the original entry FreeBASIC.</pre>
==={{header|FreeBASIC}}===
{{trans|Wren}} - original version
{{trans|Pascal}} - version with minimized multiplications
<syntaxhighlight lang="freebasic">Function isIdonealOrg(n As Uinteger) As Boolean
Dim As Uinteger a, b, c, sum
For a = 1 To n
For b = a+1 To n
If (a*b + a + b > n) Then Exit For
For c = b+1 To n
sum = a*b + b*c + a*c
If sum = n Then Return false
If sum > n Then Exit For
Next c
Next b
Next a
Return true
End Function
Function isIdoneal(n As Uinteger) As Boolean
Dim As Uinteger a, b, c, axb, ab, sum
For a = 1 To n
ab = a+a
axb = a*a
For b = a+1 To n
axb += a
ab +=1
sum = axb + b*ab
If (sum > n) Then Exit For
For c = b+1 To n
sum += ab
If (sum = n) Then Return false
If (sum > n) Then Exit For
Next c
Next b
Next a
Return true
End Function
Dim As Double t0 = Timer
Dim r As Byte = 0
Print "The 65 known Idoneal numbers:"
For n As Uinteger = 1 To 1850
If isIdonealOrg(n) Then
Print Using "#####"; n;
r += 1
If r Mod 13 = 0 Then Print
End If
Next n
Print !"\nTime:"; (Timer - t0); Chr(10)
Dim As Double t1 = Timer
For n As Uinteger = 1 To 1850
If isIdoneal(n) Then
Print Using "#####"; n;
r += 1
If r Mod 13 = 0 Then Print
End If
Next n
Print !"\n\nTime:"; (Timer - t1)
Sleep</syntaxhighlight>
{{out}}
<pre>'Tested in jdoodle.com
The 65 known Idoneal numbers:
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
0.5490732192993164 ms per run
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
0.3645658493041992 ms per run</pre>
==={{header|Liberty BASIC}}===
{{trans|XPL0}}
{{works with|Just BASIC}}
<syntaxhighlight lang="libertybasic">
' Idoneal numbers
n = 1: c = 0
do
if isIdoneal(n) then
print using("#####", n);
c = c + 1
if c mod 13 = 0 then print
end if
n = n + 1
loop until c >= 65
print
end
function isIdoneal(n)
'Return -1 if n is an Idoneal number, 0 otherwise
for a = 1 to n
for b = a + 1 to n
ab = a * b
s = a + b
if ab + s > n then
b = n
else
for c = b + 1 to n
t = ab + c * s
if t = n then isIdoneal = 0: exit function
if t > n then c = n
next
end if
next b
next a
isIdoneal = -1
end function
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
==={{header|Yabasic}}===
Line 84 ⟶ 453:
{{out}}
<pre>Same as the original entry FreeBASIC.</pre>
=={{header|C}}==
{{trans|Raku}}
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
bool isIdoneal(int n) {
int a, b, c, sum;
for (a = 1; a < n; ++a) {
for (b = a + 1; b < n; ++b) {
if (a*b + a + b > n) break;
for (c = b + 1; c < n; ++c) {
sum = a*b + b*c + a*c;
if (sum == n) return false;
if (sum > n) break;
}
}
}
return true;
}
int main() {
int n, count = 0;
for (n = 1; n <= 1850; ++n) {
if (isIdoneal(n)) {
printf("%4d ", n);
if (!(++count % 13)) printf("\n");
}
}
return 0;
}</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|C#|CSharp}}==
Line 122 ⟶ 531:
Calculations took 28.5862 ms</pre>
=={{header|
<syntaxhighlight lang="clu">idoneal = proc (n: int) returns (bool)
for a: int in int$from_to(1, n) do
for b: int in int$from_to(a+1, n) do
if (a*b + a + b > n) then exit b_high end
for c: int in int$from_to(b+1,n) do
end
except when c_high:
end
except when b_high:
end idoneal
idoneals = iter (amt: int) yields (int)
n: int := 0
while amt > 0 do
end idoneals
start_up = proc ()
po: stream := stream$primary_input()
col: int := 0
for i: int in idoneals(65) do
stream$putright(po, int$unparse(i), 5)
end
end
end start_up</syntaxhighlight>
{{out}}
<pre> 1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848</pre>
=={{header|EasyLang}}==
{{trans|Lua}}
<syntaxhighlight lang=easylang>
maxCount = 65
while count < maxCount
n += 1
idoneal = 1
a = 1
while a + 2 < n and idoneal = 1
b = a + 1
repeat
ab = a * b
sum = 0
if ab < n
c = (n - ab) div (a + b)
sum = ab + c * (b + a)
if c > b and sum = n
idoneal = 0
.
b += 1
.
until sum > n or idoneal = 0 or ab >= n
.
a += 1
.
if idoneal = 1
count += 1
write " " & n
.
.
</syntaxhighlight>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
local fn IsIdoneal( n as long ) as BOOL
long a, b, c, sum
BOOL result = NO
for a = 1 to n
for b = a + 1 to n
if ( a * b + a + b > n ) then break
for c = b + 1 to n
sum = a * b + b * c + a * c
if ( sum = n ) then result = NO : exit fn
if ( sum > n ) then break
next
next
next
result = YES
end fn = result
long r, n
r = 0
print "The 65 known Idoneal numbers:"
for n = 1 to 1850
if ( fn IsIdoneal( n ) == YES )
printf @"%5ld\b", n
r++
if r mod 13 == 0 then print
end if
next
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
The 65 known Idoneal numbers:
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
Line 199 ⟶ 654:
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<syntaxhighlight lang="go">package main
import "rcu"
func isIdoneal(n int) bool {
for a := 1; a < n; a++ {
for b := a + 1; b < n; b++ {
if a*b+a+b > n {
break
}
for c := b + 1; c < n; c++ {
sum := a*b + b*c + a*c
if sum == n {
return false
}
if sum > n {
break
}
}
}
}
return true
}
func main() {
var idoneals []int
for n := 1; n <= 1850; n++ {
if isIdoneal(n) {
idoneals = append(idoneals, n)
}
}
rcu.PrintTable(idoneals, 13, 4, false)
}</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|J}}==
Line 215 ⟶ 716:
This entry uses jq's `break` because the equivalent program using `until` is much slower.
Using
the program shown below takes about 2.5 seconds to produce the 65
idoneal numbers on a 3 GHz machine; gojq takes about 5 seconds.
For gojq, the definition of the `_nwise` helper function must be
uncommented.
Line 263 ⟶ 764:
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|Julia}}==
{{Trans|Action!}}
<syntaxhighlight lang="julia">
begin # find idoneal numbers - numbers that cannot be written as ab + bc + ac
# where 0 < a < b < c
# there are 65 known idoneal numbers
local count = 0
local maxCount = 65
local n = 0
local iNumbers = collect( 1 : maxCount )
while count < maxCount
n += 1
local idoneal = true
local a = 1
while ( a + 2 ) < n && idoneal
local b = a + 1
while true
local ab = a * b
local sum = 0
if ab < n
local c = ( n - ab ) ÷ ( a + b )
sum = ab + ( c * ( b + a ) )
if c > b && sum == n
idoneal = false
end
b += 1
end
if sum > n || idoneal == 0 || ab >= n
break
end
end
a += 1
end
if idoneal
count += 1
iNumbers[ count ] = n
end
end
println( iNumbers )
end
</syntaxhighlight>
{{out}}
<pre>
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93, 102, 105, 112, 120, 130, 133, 165, 168, 177, 190, 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, 1848]
</pre>
=={{header|Lua}}==
{{Trans|Action!}}
<syntaxhighlight lang="lua">
do -- find idoneal numbers - numbers that cannot be written as ab + bc + ac
-- where 0 < a < b < c
-- there are 65 known idoneal numbers
local count = 0
local maxCount = 65
local n = 0
while count < maxCount do
n = n + 1
local idoneal = true
local a = 1
while ( a + 2 ) < n and idoneal do
local b = a + 1
repeat
local ab = a * b
local sum = 0
if ab < n then
local c = math.floor( ( n - ab ) / ( a + b ) )
sum = ab + ( c * ( b + a ) )
if c > b and sum == n then
idoneal = false
end
b = b + 1
end
until sum > n or not idoneal or ab >= n
a = a + 1
end
if idoneal then
count = count + 1
io.write( string.format( " %4d", n ) )
if count % 13 == 0 then io.write( "\n" ) end
end
end
end
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|MiniScript}}==
<syntaxhighlight lang="miniscript">
isIdoneal = function(n)
for a in range(1, n)
for b in range(a + 1, n)
if a * b + a + b > n then break
for c in range(b + 1, n)
sum3 = a * b + b * c + a * c
if sum3 == n then return false
if sum3 > n then break
end for
end for
end for
return true
end function
idoneals = []
for n in range(1, 2000)
if isIdoneal(n) then idoneals.push(n)
end for
print idoneals.join(", ")
</syntaxhighlight>
{{out}}
<pre>
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93, 102, 105, 112, 120, 130, 133, 165, 168, 177, 190, 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, 1848
</pre>
=={{header|Nim}}==
To do something different, we use a sieve. This is more efficient as the computations are done only once. But, in this case, this doesn’t change a lot.
<syntaxhighlight lang=Nim>import std/[algorithm, math, strformat]
const N = 2000
var isIdoneal: array[1..N, bool]
isIdoneal.fill(true)
for a in 1..sqrt(N / 3).int:
var p = a * (a + 1)
for b in (a + 1)..(N div (3 * a)):
var n = p + (a + b) * (b + 1)
while n <= N:
isIdoneal[n] = false
inc n, a + b
inc p, a
var idx = 0
for n in 1..N:
if isIdoneal[n]:
inc idx
stdout.write &"{n:>4}"
stdout.write if idx mod 13 == 0: '\n' else: ' '
echo()
</syntaxhighlight>
{{out}}
<pre> 1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
Line 402 ⟶ 1,059:
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
2.036 ms per run</pre>
=={{header|Perl}}==
<syntaxhighlight lang="perl" line>use v5.36;
use enum qw(False True);
sub table ($c, @V) { my $t = $c * (my $w = 5); ( sprintf( ('%'.$w.'d')x@V, @V) ) =~ s/.{1,$t}\K/\n/gr }
sub is_idoneal ($n) {
LOOP:
for my $a (1 .. $n) {
for my $b ($a+1 .. $n) {
last if $a*$b + $a + $b > $n;
for my $c ($b+1 .. $n) {
return False if $n == (my $sum = $a*$b + $b*$c + $c*$a);
last if $sum > $n;
}
}
}
True
}
say table 10, grep { is_idoneal $_ } 1..1850;</syntaxhighlight>
{{out}}
<pre> 1 2 3 4 5 6 7 8 9 10
12 13 15 16 18 21 22 24 25 28
30 33 37 40 42 45 48 57 58 60
70 72 78 85 88 93 102 105 112 120
130 133 165 168 177 190 210 232 240 253
273 280 312 330 345 357 385 408 462 520
760 840 1320 1365 1848</pre>
=={{header|Phix}}==
Line 432 ⟶ 1,119:
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|PL/0}}==
PL/0 goes for minimalism and so doesn't have a boolean type or "and", "or" and "not" operators.
<syntaxhighlight lang="pascal">
const maxcount = 65;
var count, n, idoneal, a, b, c, ab, aplusb, nminusa, sum, bagain;
begin
count := 0;
n := 0;
while count < maxcount do begin
n := n + 1;
idoneal := 1;
a := 0;
while a < n * idoneal do begin
a := a + 1;
nminusa := n - a;
b := a;
if b <= nminusa then begin
bagain := idoneal;
while bagain = 1 do begin
b := b + 1;
ab := a * b;
aplusb := a + b;
c := ( n - ab ) / aplusb;
sum := ab + ( c * aplusb );
idoneal := 0;
if c <= b then idoneal := 1;
if sum <> n then idoneal := 1;
bagain := 0;
if b <= nminusa then if sum <= n then bagain := idoneal
end
end;
end;
if idoneal = 1 then begin
! n;
count := count + 1
end
end
end.
</syntaxhighlight>
{{out}}
<pre>
1
2
3
4
5
6
7
8
9
10
12
...
760
840
1320
1365
1848
</pre>
=={{header|PL/M}}==
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
<syntaxhighlight lang="plm">
100H: /* FIND IDONEAL NUMBERS - NUMBERS THAT CANNOT BE WRITTEN */
/* AS AB + BC + AC WHERE 0 < A < B < C */
/* THERE ARE 65 KNOWN IDONEAL NUMBERS */
/* CP/M BDOS SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* TASK */
DECLARE TRUE LITERALLY '0FFH', FALSE LITERALLY '0';
DECLARE ( COUNT, N, A, B, C, AB, SUM ) ADDRESS;
DECLARE ( IDONEAL, FINISHED ) BYTE;
DECLARE MAX$COUNT LITERALLY '65';
COUNT, N = 0;
DO WHILE COUNT < MAX$COUNT;
N = N + 1;
IDONEAL = TRUE;
A = 1;
DO WHILE ( A + 2 ) < N AND IDONEAL;
B = A + 1;
FINISHED = FALSE;
DO WHILE NOT FINISHED;
AB = A * B;
SUM = 0;
IF AB < N THEN DO;
C = ( N - AB ) / ( A + B );
SUM = AB + ( C * ( B + A ) );
IF C > B AND SUM = N THEN IDONEAL = FALSE;
B = B + 1;
END;
FINISHED = SUM > N OR NOT IDONEAL OR AB >= N;
END;
A = A + 1;
END;
IF IDONEAL THEN DO;
CALL PR$CHAR( ' ' );
IF N < 10 THEN CALL PR$CHAR( ' ' );
IF N < 100 THEN CALL PR$CHAR( ' ' );
IF N < 1000 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( N );
IF ( COUNT := COUNT + 1 ) MOD 13 = 0 THEN CALL PR$NL;
END;
END;
EOF
</syntaxhighlight>
{{out}}
<pre>
1 2 3 4 5 6 7 8 9 10 12 13 15
16 18 21 22 24 25 28 30 33 37 40 42 45
48 57 58 60 70 72 78 85 88 93 102 105 112
120 130 133 165 168 177 190 210 232 240 253 273 280
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
Line 493 ⟶ 1,314:
273 280 312 330 345 357 385 408 462 520
760 840 1320 1365 1848</pre>
=={{header|RPL}}==
{{trans|Python}}
{{works with|Halcyon Calc|4.2.7}}
{| class="wikitable"
! RPL code
! Comment
|-
|
≪ → num
≪ 1 SF
1 num FOR a
a 1 + num FOR b
IF a b DUP2 * + + num > THEN
num 'b' STO
ELSE b 1 + num FOR c
a b * b c * + a c * +
IF DUP num == THEN
DROP 1 CF num DUP DUP 'a' STO 'b' STO 'c' STO
ELSE IF num > THEN
num 'c' STO END
END
NEXT END
NEXT NEXT
1 FS?
≫ ≫ ‘IDNL?’ STO
|
''' IDNL?''' ''( n -- boolean )''
Return value will be given by flag #1
for a in range(1, num):
for b in range(a + 1, num):
if a * b + a + b > num:
break
for c in range(b + 1, num):
sum3 = a * b + b * c + a * c
if sum3 == num:
return False
if sum3 > num:
break
.
.
.
Return boolean value
.
|}
{{in}}
<pre>
≪ {} 1 255 FOR n IF n IDNL? THEN n + END NEXT ≫ EVAL
≪ {} 256 2000 FOR n IF n IDNL? THEN n + END NEXT ≫ EVAL
</pre>
{{out}}
<pre>
2: { 1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24 25 28 30 33 37 40 42 45 48 57 58 60 70 72 78 85 88 93 102 105 112 120 130 133 165 168 177 190 210 232 240 253 }
1: { 273 280 312 330 345 357 385 408 462 520 760 840 1320 1365 1848 }
</pre>
=={{header|Swift}}==
Line 537 ⟶ 1,413:
{{trans|Raku}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
var isIdoneal = Fn.new { |n|
Line 605 ⟶ 1,481:
312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">SetOfNonIdonealNumbers = Flatten@Table[If[0 < a && a < b && b < c, a*b + b*c + a*c, ## &[]], {a, 1, 300}, {b, 1, 300}, {c, 1, 300}];
DeleteCases[Range[120000], Alternatives @@ SetOfNonIdonealNumbers] (*a,b,c up to 300 can't completely cover numbers above 126 581*)</syntaxhighlight>
{{out}}<pre>{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93, 102, 105, 112, 120, 130, 133, 165, 168, 177, 190, 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, 1848}</pre>
| |||