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

Author

K. D. Bajpai, Jun 28 2015

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Magma

[ n: n in [1..10^4] |  IsSquare(&+Intseq(n)^3 + n) ] ;

Mathematica

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

PARI

for(n = 1, 10^5, if(issquare(sumdigits(n)^3 + n), print1(n, ", ")))