A259489 Numbers n such that n plus the cube of sum of digits of n is a perfect square.

17, 38, 131, 171, 360, 392, 500, 512, 605, 729, 863, 1031, 1035, 1481, 1737, 1994, 2156, 2268, 2483, 2513, 2520, 2732, 2817, 3011, 3240, 3384, 3449, 3710, 3881, 3923, 4032, 4100, 4112, 4145, 4572, 5193, 5456, 5598, 5720, 5832, 5903, 5924, 7164, 7388, 7625, 7631

Offset

1,1

Comments

All the terms are congruent to 2 or 0 (mod 3).

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(3) = 131: 131 + (1 + 3 + 1)^3 = 256 = 16^2.
a(4) = 171: 171 + (1 + 7 + 1)^3 = 900 = 30^2.

Mathematica

Select[Range[50000], IntegerQ[Sqrt[# +Plus@@(IntegerDigits[#])^3]]&]

Prog

(PARI) for(n = 1, 10^5, if(issquare(sumdigits(n)^3 + n), print1(n, ", ")))
(Magma) [ n: n in [1..10^4] |  IsSquare(&+Intseq(n)^3 + n) ] ;

Crossrefs

Cf. A007494, A052034, A061309, A091365, A091366.

Sequence in context: A139579 A293206 A125248 * A226127 A156777 A070142

Adjacent sequences: A259486 A259487 A259488 * A259490 A259491 A259492

Keyword

nonn,base

Author

K. D. Bajpai, Jun 28 2015

Status

approved