A236749 -id:A236749 - cp's OEIS frontend

A236748 Positive integers k such that k^2 divided by the digital sum of k is a square.

1, 4, 9, 10, 18, 22, 27, 36, 40, 45, 54, 63, 72, 81, 88, 90, 100, 108, 112, 117, 126, 130, 135, 144, 153, 162, 171, 180, 196, 202, 207, 216, 220, 225, 234, 243, 252, 261, 268, 270, 306, 310, 315, 324, 333, 342, 351, 360, 376, 400, 405, 414, 423, 432, 441

Offset: 1

Colin Barker, Jan 30 2014

Subsequence of A028839 (sum of digits of n is a square). - Jon Perry and Michel Marcus, Oct 30 2014
A028839 is the sequence of positive integers such that n^2 divided by the sum of the digits is a rational square. For this sequence, it is required to be an integer square. - Franklin T. Adams-Watters, Oct 30 2014
The sequence is infinite since if m = 10^j then m^2 / digitsum(m) = m^2. - Marius A. Burtea, Dec 21 2018

			153 is in the sequence because the digital sum of 153 is 9, and 153^2/9 = 2601 = 51^2.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A001102, A007953, A236749, A236750, A236751.

Cf. A028839.

[n: n in [1..1500] | IsIntegral((n^2)/(&+Intseq(n))) and IsSquare((n^2)/(&+Intseq(n)))]; // Marius A. Burtea, Dec 21 2018

filter:= n -> issqr(n^2/convert(convert(n,base,10),`+`)):
select(filter, [$1..10000]); # Robert Israel, Oct 30 2014

Select[Range[500],IntegerQ[Sqrt[#^2/Total[IntegerDigits[#]]]]&] (* Harvey P. Dale, Nov 19 2014 *)

s=[]; for(n=1, 600, d=sumdigits(n); if(n^2%d==0 && issquare(n^2\d), s=concat(s, n))); s

A236750 Positive integers k such that k^3 divided by the digital sum of k is a square.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 81, 100, 144, 150, 192, 196, 200, 225, 242, 288, 300, 320, 324, 375, 400, 441, 484, 500, 512, 600, 640, 648, 700, 704, 735, 800, 832, 882, 900, 960, 1014, 1088, 1200, 1250, 1452, 1458, 1521, 1815, 2023, 2025, 2028

Offset: 1

Colin Barker, Jan 30 2014

The sequence is infinite since if m = 10^(2*j) then m^3 / digitsum(m) = m^(6*k). - Marius A. Burtea, Dec 21 2018

			192 is in the sequence because the digital sum of 192 is 12, and 192^3/12 = 589824 = 768^2.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A001102, A007953, A236748, A236749, A236751.

[n: n in [1..1500] | IsIntegral((n^3)/(&+Intseq(n))) and IsSquare((n^3)/(&+Intseq(n)))]; // Marius A. Burtea, Dec 21 2018

s=[]; for(n=1, 5000, d=sumdigits(n); if(n^3%d==0 && issquare(n^3\d), s=concat(s, n))); s

A236751 Positive integers n such that n^3 divided by the digital sum of n is a cube.

Original entry on oeis.org

1, 8, 10, 26, 44, 62, 80, 100, 116, 134, 152, 170, 206, 224, 242, 260, 314, 332, 350, 404, 422, 440, 512, 530, 602, 620, 710, 800, 999, 1000, 1016, 1034, 1052, 1070, 1106, 1124, 1142, 1160, 1214, 1232, 1250, 1304, 1322, 1340, 1412, 1430, 1502, 1520, 1610

Offset: 1

Colin Barker, Jan 30 2014

			152 is in the sequence because the digital sum of 152 is 8, and 152^3/8 = 438976 = 76^3.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A007953, A236748, A236749, A236750.

s=[]; for(n=1, 3000, d=sumdigits(n); if(n^3%d==0 && ispower(n^3\d, 3), s=concat(s, n))); s

cp's OEIS Frontend

A236748 Positive integers k such that k^2 divided by the digital sum of k is a square.

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A236750 Positive integers k such that k^3 divided by the digital sum of k is a square.

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Author

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Magma

PARI

A236751 Positive integers n such that n^3 divided by the digital sum of n is a cube.

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Author

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Programs

PARI