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

1,2

Comments

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

Links

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

Example

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

Maple

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

Mathematica

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

Prog

(PARI) s=[]; for(n=1, 600, d=sumdigits(n); if(n^2%d==0 && issquare(n^2\d), s=concat(s, n))); s
(Magma) [n: n in [1..1500] | IsIntegral((n^2)/(&+Intseq(n))) and IsSquare((n^2)/(&+Intseq(n)))]; // Marius A. Burtea, Dec 21 2018

Crossrefs

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

Cf. A028839.

Sequence in context: A305231 A312832 A236652 * A102837 A356417 A004631

Adjacent sequences: A236745 A236746 A236747 * A236749 A236750 A236751

Keyword

nonn,base

Author

Colin Barker, Jan 30 2014

Status

approved