Square but not cube
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Show the first 30 positive integers which are squares but not cubes of such integers.
Optionally, show also the first 3 positive integers which are both squares and cubes - and mark them as such.
Contents
ALGOL 68[edit]
Avoids computing cube roots.
BEGIN
# list the first 30 numbers that are squares but not cubes and also #
# show the numbers that are both squares and cubes #
INT count := 0;
INT c := 1;
INT c3 := 1;
FOR s WHILE count < 30 DO
INT sq = s * s;
WHILE c3 < sq DO
c +:= 1;
c3 := c * c * c
OD;
print( ( whole( sq, -5 ) ) );
IF c3 = sq THEN
# the square is also a cube #
print( ( " is also the cube of ", whole( c, -5 ) ) )
ELSE
# square only #
count +:= 1
FI;
print( ( newline ) )
OD
END
- Output:
1 is also the cube of 1
4
9
16
25
36
49
64 is also the cube of 4
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729 is also the cube of 9
784
841
900
961
1024
1089
AppleScript[edit]
on run
script listing
on |λ|(x)
set sqr to x * x
set strSquare to sqr as text
if isCube(sqr) then
strSquare & " (also cube)"
else
strSquare
end if
end |λ|
end script
unlines(map(listing, ¬
enumFromTo(1, 33)))
end run
-- isCube :: Int -> Bool
on isCube(x)
x = (round (x ^ (1 / 3))) ^ 3
end isCube
-- GENERIC FUNCTIONS -------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
- Output:
1 (also cube) 4 9 16 25 36 49 64 (also cube) 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 (also cube) 784 841 900 961 1024 1089
AWK[edit]
# syntax: GAWK -f SQUARE_BUT_NOT_CUBE.AWK
BEGIN {
while (n < 30) {
sqpow = ++square ^ 2
if (is_cube(sqpow) == 0) {
n++
printf("%4d\n",sqpow)
}
else {
printf("%4d is square and cube\n",sqpow)
}
}
exit(0)
}
function is_cube(x, i) {
for (i=1; i<=x; i++) {
if (i ^ 3 == x) {
return(1)
}
}
return(0)
}
- Output:
1 is square and cube 4 9 16 25 36 49 64 is square and cube 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 is square and cube 784 841 900 961 1024 1089
C[edit]
#include <stdio.h>
#include <math.h>
int main() {
int n = 1, count = 0, sq, cr;
for ( ; count < 30; ++n) {
sq = n * n;
cr = (int)cbrt((double)sq);
if (cr * cr * cr != sq) {
count++;
printf("%d\n", sq);
}
else {
printf("%d is square and cube\n", sq);
}
}
return 0;
}
- Output:
Same as Ring example.
F#[edit]
let rec fN n g φ=if φ<31 then match compare(n*n)(g*g*g) with | -1->printfn "%d"(n*n);fN(n+1) g (φ+1)
| 0->printfn "%d cube and square"(n*n);fN(n+1)(g+1)φ
| 1->fN n (g+1) φ
fN 1 1 1
- Output:
1 cube and square 4 9 16 25 36 49 64 cube and square 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 cube and square 784 841 900 961 1024 1089
Factor[edit]
USING: combinators interpolate io kernel prettyprint math
math.functions math.order pair-rocket ;
IN: rosetta-code.square-but-not-cube
: fn ( s c n -- s' c' n' )
dup 31 < [
2over [ sq ] [ 3 ^ ] bi* <=> {
+lt+ => [ [ dup sq . 1 + ] 2dip 1 + fn ]
+eq+ => [ [ dup sq [I ${} cube and squareI] nl 1 + ] [ 1 + ] [ ] tri* fn ]
+gt+ => [ [ 1 + ] dip fn ]
} case
] when ;
1 1 1 fn 3drop
- Output:
1 cube and square 4 9 16 25 36 49 64 cube and square 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 cube and square 784 841 900 961 1024 1089
Go[edit]
package main
import (
"fmt"
"math"
)
func main() {
for n, count := 1, 0; count < 30; n++ {
sq := n * n
cr := int(math.Cbrt(float64(sq)))
if cr*cr*cr != sq {
count++
fmt.Println(sq)
} else {
fmt.Println(sq, "is square and cube")
}
}
}
- Output:
1 is square and cube 4 9 16 25 36 49 64 is square and cube 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 is square and cube 784 841 900 961 1024 1089
Haskell[edit]
import Data.List (partition, sortBy)
import Control.Monad (join)
import Data.Ord (comparing)
isCube :: Int -> Bool
isCube n = n == round (fromIntegral n ** (1 / 3)) ^ 3
both, only :: [Int]
(both, only) = partition isCube $ join (*) <$> [1 ..]
-- TEST -----------------------------------------------------------
main :: IO ()
main =
(putStrLn . unlines) $
uncurry ((++) . show) <$>
sortBy
(comparing fst)
((flip (,) " (also cube)" <$> take 3 both) ++ (flip (,) "" <$> take 30 only))
Or simply
import Control.Monad (join)
cubeRoot :: Int -> Int
cubeRoot = round . (** (1 / 3)) . fromIntegral
isCube :: Int -> Bool
isCube = (==) <*> ((^ 3) . cubeRoot)
-- TEST ---------------------------------------------
main :: IO ()
main =
(putStrLn . unlines) $
(\x ->
show x ++
if isCube x
then concat [" (also cube of ", show (cubeRoot x), ")"]
else []) <$>
take 33 (join (*) <$> [1 ..])
Or, if we prefer a finite series to an infinite one
import Control.Applicative (liftA2)
isCube :: Int -> Bool
isCube = (==) <*> ((^ 3) . round . (** (1 / 3)) . fromIntegral)
squares :: Int -> Int -> [Int]
squares m n = (>>= id) (*) <$> [m .. n]
-- TEST ------------------------------------------------------------
main :: IO ()
main = (putStrLn . unlines) $ liftA2 (++) show label <$> squares 1 33
label :: Int -> String
label n
| isCube n = " (also cube)"
| otherwise = ""
- Output:
1 (also cube) 4 9 16 25 36 49 64 (also cube) 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 (also cube) 784 841 900 961 1024 1089
IS-BASIC[edit]
100 PROGRAM "Square.bas"
110 LET SQNOTCB,SQANDCB,SQNUM,CBNUM,CBN,SQN,D1=0:LET SQD,D2=1
120 DO
130 LET SQN=SQN+1:LET SQNUM=SQNUM+SQD:LET SQD=SQD+2
140 IF SQNUM>CBNUM THEN
150 LET CBN=CBN+1:LET CBNUM=CBNUM+D2
160 LET D1=D1+6:LET D2=D2+D1
170 END IF
180 IF SQNUM<>CBNUM THEN
190 PRINT SQNUM:LET SQNOTCB=SQNOTCB+1
200 ELSE
210 PRINT SQNUM,SQN;"*";SQN;"=";CBN;"*";CBN;"*";CBN
220 LET SQANDCB=SQANDCB+1
230 END IF
240 LOOP UNTIL SQNOTCB>=30
250 PRINT SQANDCB;"where numbers are square and cube."
JavaScript[edit]
(() => {
'use strict';
const main = () =>
unlines(map(
x => x.toString() + (
isCube(x) ? (
` (cube of ${cubeRootInt(x)} and square of ${
Math.pow(x, 1/2)
})`
) : ''
),
map(x => x * x, enumFromTo(1, 33))
));
// isCube :: Int -> Bool
const isCube = n =>
n === Math.pow(cubeRootInt(n), 3);
// cubeRootInt :: Int -> Int
const cubeRootInt = n => Math.round(Math.pow(n, 1 / 3));
// GENERIC FUNCTIONS ----------------------------------
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
m <= n ? iterateUntil(
x => n <= x,
x => 1 + x,
m
) : [];
// iterateUntil :: (a -> Bool) -> (a -> a) -> a -> [a]
const iterateUntil = (p, f, x) => {
const vs = [x];
let h = x;
while (!p(h))(h = f(h), vs.push(h));
return vs;
};
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f);
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// MAIN ---
return main();
})();
- Output:
1 (cube of 1 and square of 1) 4 9 16 25 36 49 64 (cube of 4 and square of 8) 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 (cube of 9 and square of 27) 784 841 900 961 1024 1089
Julia[edit]
iscube(n) = n == round(Int, cbrt(n))^3
println(collect(Iterators.take((n^2 for n in 1:10^6 if !iscube(n^2)), 30)))
- Output:
[4, 9, 16, 25, 36, 49, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Kotlin[edit]
// Version 1.2.60
fun main(args: Array<String>) {
var n = 1
var count = 0
while (count < 30) {
val sq = n * n
val cr = Math.cbrt(sq.toDouble()).toInt()
if (cr * cr * cr != sq) {
count++
println(sq)
}
else {
println("$sq is square and cube")
}
n++
}
}
- Output:
Same as Ring example.
Pascal[edit]
Only using addition :-)
program SquareButNotCube;
var
sqN,
sqDelta,
SqNum,
cbN,
cbDelta1,
cbDelta2,
CbNum,
CountSqNotCb,
CountSqAndCb : NativeUint;
begin
CountSqNotCb := 0;
CountSqAndCb := 0;
SqNum := 0;
CbNum := 0;
cbN := 0;
sqN := 0;
sqDelta := 1;
cbDelta1 := 0;
cbDelta2 := 1;
repeat
inc(sqN);
inc(sqNum,sqDelta);
inc(sqDelta,2);
IF sqNum>cbNum then
Begin
inc(cbN);
cbNum := cbNum+cbDelta2;
inc(cbDelta1,6);// 0,6,12,18...
inc(cbDelta2,cbDelta1);//1,7,19,35...
end;
IF sqNum <> cbNUm then
Begin
writeln(sqNum :25);
inc(CountSqNotCb);
end
else
Begin
writeln(sqNum:25,sqN:10,'*',sqN,' = ',cbN,'*',cbN,'*',cbN);
inc(CountSqANDCb);
end;
until CountSqNotCb >= 30;//sqrt(High(NativeUint));
writeln(CountSqANDCb,' where numbers are square and cube ');
end.
- Output:
1 1*1 = 1*1*1
4
9
16
25
36
49
64 8*8 = 4*4*4
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729 27*27 = 9*9*9
784
841
900
961
1024
1089
3 where numbers are square and cube
// there are 1625 numbers which are square and cube < High(Uint64)
//18412815093994140625 4291015625*4291015625 = 2640625*2640625*2640625
Perl[edit]
Hash[edit]
Use a hash to track state (and avoid floating-point math).
while ($cnt < 30) {
$n++;
$h{$n**2}++;
$h{$n**3}--;
$cnt++ if $h{$n**2} > 0;
}
print "First 30 positive integers that are a square but not a cube:\n";
print "$_ " for sort { $a <=> $b } grep { $h{$_} == 1 } keys %h;
print "\n\nFirst 3 positive integers that are both a square and a cube:\n";
print "$_ " for sort { $a <=> $b } grep { $h{$_} == 0 } keys %h;
- Output:
First 30 positive integers that are a square but not a cube: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 First 3 positive integers that are both a square and a cube: 1 64 729
Generators[edit]
A more general approach involving generators/closures to implement 'lazy' lists as in the Perl 6 example. Using ideas and code from the very similar Generator exponential task. Output is the same as previous.
# return an anonymous subroutine that generates stream of specified powers
sub gen_pow {
my $m = shift;
my $e = 1;
return sub { return $e++ ** $m; };
}
# return an anonymous subroutine generator that filters output from supplied generators g1 and g2
sub gen_filter {
my($g1, $g2) = @_;
my $v1;
my $v2 = $g2->();
return sub {
while (1) {
$v1 = $g1->();
$v2 = $g2->() while $v1 > $v2;
return $v1 unless $v1 == $v2;
}
};
}
my $pow2 = gen_pow(2);
my $pow3 = gen_pow(3);
my $squares_without_cubes = gen_filter($pow2, $pow3);
print "First 30 positive integers that are a square but not a cube:\n";
print $squares_without_cubes->() . ' ' for 1..30;
my $pow6 = gen_pow(6);
print "\n\nFirst 3 positive integers that are both a square and a cube:\n";
print $pow6->() . ' ' for 1..3;
Perl 6[edit]
my @square-and-cube = map { .⁶ }, 1..Inf;
my @square-but-not-cube = (1..Inf).map({ .² }).grep({ $_ ∉ @square-and-cube[^@square-and-cube.first: * > $_, :k]});
put "First 30 positive integers that are a square but not a cube: \n", @square-but-not-cube[^30];
put "\nFirst 15 positive integers that are both a square and a cube: \n", @square-and-cube[^15];
- Output:
First 30 positive integers that are a square but not a cube: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 First 15 positive integers that are both a square and a cube: 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809 7529536 11390625
Python[edit]
# nonCubeSquares :: Int -> [(Int, Bool)]
def nonCubeSquares(n):
upto = enumFromTo(1)
ns = upto(n)
setCubes = set(x ** 3 for x in ns)
ms = upto(n + len(set(x * x for x in ns).intersection(
setCubes
)))
return list(tuple([x * x, x in setCubes]) for x in ms)
# squareListing :: [(Int, Bool)] -> [String]
def squareListing(xs):
justifyIdx = justifyRight(len(str(1 + len(xs))))(' ')
justifySqr = justifyRight(1 + len(str(xs[-1][0])))(' ')
return list(
'(' + str(1 + idx) + '^2 = ' + str(n) +
' = ' + str(round(n ** (1 / 3))) + '^3)' if bln else (
justifyIdx(1 + idx) + ' ->' +
justifySqr(n)
)
for idx, (n, bln) in enumerate(xs)
)
def main():
print(
unlines(
squareListing(
nonCubeSquares(30)
)
)
)
# GENERIC ------------------------------------------------------------------
# enumFromTo :: Int -> Int -> [Int]
def enumFromTo(m):
return lambda n: list(range(m, 1 + n))
# justifyRight :: Int -> Char -> String -> String
def justifyRight(n):
return lambda cFiller: lambda a: (
((n * cFiller) + str(a))[-n:]
)
# unlines :: [String] -> String
def unlines(xs):
return '\n'.join(xs)
main()
- Output:
(1^2 = 1 = 1^3) 2 -> 4 3 -> 9 4 -> 16 5 -> 25 6 -> 36 7 -> 49 (8^2 = 64 = 4^3) 9 -> 81 10 -> 100 11 -> 121 12 -> 144 13 -> 169 14 -> 196 15 -> 225 16 -> 256 17 -> 289 18 -> 324 19 -> 361 20 -> 400 21 -> 441 22 -> 484 23 -> 529 24 -> 576 25 -> 625 26 -> 676 (27^2 = 729 = 9^3) 28 -> 784 29 -> 841 30 -> 900 31 -> 961 32 -> 1024 33 -> 1089
REXX[edit]
Programming note: extra code was added to support an additional output format (see the 2nd output section).
/*REXX pgm shows N ints>0 that are squares and not cubes, & which are squares and cubes.*/
numeric digits 20 /*be able to handle some large numbers.*/
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N=30 /*Not specified? Then use the default.*/
sqcb= N<0 /*N negative? Then show squares & cubes*/
N = abs(N) /*define N to be the absolute value. */
w= length(N) + 3 /*W: used for aligning output columns.*/
say ' count ' /*display the 1st line of the title. */
say ' ─────── ' /* " " 2nd " " " " */
@.= 0 /*@: stemmed array for computed cubes.*/
#= 0; ##= 0 /*count (integer): squares & not cubes.*/
do j=1 until #==N | ##==N /*loop 'til enough " " " " */
sq= j*j; cube= sq*j; @.cube= 1 /*compute the square of J and the cube.*/
if @.sq then do
##= ## + 1 /*bump the counter of squares and cubs.*/
if \sqcb then counter= left('', 12) /*don't show this counter.*/
else counter= center(##, 12) /* do " " " */
say counter right(sq, 3*w) 'is a square and a cube'
end
else do
if sqcb then iterate
#= # + 1 /*bump the counter of squares & ¬ cubes*/
say center(#, 12) right(sq, 3*w) 'is a square and not a cube'
end
end /*j*/ /*stick a fork in it, we're all done. */
- output when using the default input:
count
───────
1 is a square and a cube
1 4 is a square and not a cube
2 9 is a square and not a cube
3 16 is a square and not a cube
4 25 is a square and not a cube
5 36 is a square and not a cube
6 49 is a square and not a cube
64 is a square and a cube
7 81 is a square and not a cube
8 100 is a square and not a cube
9 121 is a square and not a cube
10 144 is a square and not a cube
11 169 is a square and not a cube
12 196 is a square and not a cube
13 225 is a square and not a cube
14 256 is a square and not a cube
15 289 is a square and not a cube
16 324 is a square and not a cube
17 361 is a square and not a cube
18 400 is a square and not a cube
19 441 is a square and not a cube
20 484 is a square and not a cube
21 529 is a square and not a cube
22 576 is a square and not a cube
23 625 is a square and not a cube
24 676 is a square and not a cube
729 is a square and a cube
25 784 is a square and not a cube
26 841 is a square and not a cube
27 900 is a square and not a cube
28 961 is a square and not a cube
29 1024 is a square and not a cube
30 1089 is a square and not a cube
- output when using the input of: -55
count
───────
1 1 is a square and a cube
2 64 is a square and a cube
3 729 is a square and a cube
4 4096 is a square and a cube
5 15625 is a square and a cube
6 46656 is a square and a cube
7 117649 is a square and a cube
8 262144 is a square and a cube
9 531441 is a square and a cube
10 1000000 is a square and a cube
11 1771561 is a square and a cube
12 2985984 is a square and a cube
13 4826809 is a square and a cube
14 7529536 is a square and a cube
15 11390625 is a square and a cube
16 16777216 is a square and a cube
17 24137569 is a square and a cube
18 34012224 is a square and a cube
19 47045881 is a square and a cube
20 64000000 is a square and a cube
21 85766121 is a square and a cube
22 113379904 is a square and a cube
23 148035889 is a square and a cube
24 191102976 is a square and a cube
25 244140625 is a square and a cube
26 308915776 is a square and a cube
27 387420489 is a square and a cube
28 481890304 is a square and a cube
29 594823321 is a square and a cube
30 729000000 is a square and a cube
31 887503681 is a square and a cube
32 1073741824 is a square and a cube
33 1291467969 is a square and a cube
34 1544804416 is a square and a cube
35 1838265625 is a square and a cube
36 2176782336 is a square and a cube
37 2565726409 is a square and a cube
38 3010936384 is a square and a cube
39 3518743761 is a square and a cube
40 4096000000 is a square and a cube
41 4750104241 is a square and a cube
42 5489031744 is a square and a cube
43 6321363049 is a square and a cube
44 7256313856 is a square and a cube
45 8303765625 is a square and a cube
46 9474296896 is a square and a cube
47 10779215329 is a square and a cube
48 12230590464 is a square and a cube
49 13841287201 is a square and a cube
50 15625000000 is a square and a cube
51 17596287801 is a square and a cube
52 19770609664 is a square and a cube
53 22164361129 is a square and a cube
54 24794911296 is a square and a cube
55 27680640625 is a square and a cube
Ring[edit]
# Project : Square but not cube
limit = 30
num = 0
sq = 0
while num < limit
sq = sq + 1
sqpow = pow(sq,2)
flag = iscube(sqpow)
if flag = 0
num = num + 1
see sqpow + nl
else
see "" + sqpow + " is square and cube" + nl
ok
end
func iscube(cube)
for n = 1 to cube
if pow(n,3) = cube
return 1
ok
next
return 0
Output:
1 is square and cube 4 9 16 25 36 49 64 is square and cube 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 is square and cube 784 841 900 961 1024 1089
Ruby[edit]
#!/usr/bin/env ruby
class PowIt
:next
def initialize
@next = 1;
end
end
class SquareIt < PowIt
def next
result = @next ** 2
@next += 1
return result
end
end
class CubeIt < PowIt
def next
result = @next ** 3
@next += 1
return result
end
end
squares = []
hexponents = []
squit = SquareIt.new
cuit = CubeIt.new
s = squit.next
c = cuit.next
while (squares.length < 30 || hexponents.length < 3)
if s < c
squares.push(s) if squares.length < 30
s = squit.next
elsif s == c
hexponents.push(s) if hexponents.length < 3
s = squit.next
c = cuit.next
else
c = cuit.next
end
end
puts "Squares:"
puts squares.join(" ")
puts "Square-and-cubes:"
puts hexponents.join(" ")
- Output:
Squares: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 Square-and-cubes: 1 64 729
Sidef[edit]
var square_and_cube = Enumerator({|f|
1..Inf -> each {|n| f(n**6) }
})
var square_but_not_cube = Enumerator({|f|
1..Inf -> lazy.map {|n| n**2 }.grep {|n| !n.is_power(3) }.each {|n| f(n) }
})
say "First 30 positive integers that are a square but not a cube:"
say square_but_not_cube.first(30).join(' ')
say "First 15 positive integers that are both a square and a cube:"
say square_and_cube.first(15).join(' ')
- Output:
First 30 positive integers that are a square but not a cube: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 First 15 positive integers that are both a square and a cube: 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809 7529536 11390625
zkl[edit]
println("First 30 positive integers that are a square but not a cube:");
squareButNotCube:=(1).walker(*).tweak(fcn(n){
sq,cr := n*n, sq.toFloat().pow(1.0/3).round(); // cube root(64)<4
if(sq==cr*cr*cr) Void.Skip else sq
});
squareButNotCube.walk(30).concat(",").println("\n");
println("First 15 positive integers that are both a square and a cube:");
println((1).walker(*).tweak((1).pow.unbind().fp1(6)).walk(15));
- Output:
First 30 positive integers that are a square but not a cube: 4,9,16,25,36,49,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,784,841,900,961,1024,1089 First 15 positive integers that are both a square and a cube: L(1,64,729,4096,15625,46656,117649,262144,531441,1000000,1771561,2985984,4826809,7529536,11390625
