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

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

Author

Colin Barker, Jan 30 2014

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Magma

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

PARI

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