A240128 Number of partitions of n such that the sum of cubes of the parts is a cube.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 3, 4, 4, 4, 3, 3, 4, 4, 5, 12, 9, 14, 13, 13, 16, 17, 30, 34, 33, 34, 37, 50, 57, 64, 73, 99, 101, 114, 125, 141, 187, 193, 226, 264, 286, 326, 365, 456, 506, 565, 655, 742, 809, 911, 1071, 1233, 1392, 1506, 1744, 2046

Offset: 0

Author

Clark Kimberling, Apr 02 2014

Keywords

• nonn

Examples

			a(17) counts these 4 partitions:  [17], [4,3,3,1,1,1,1,1,1,1], [4,3,2,2,2,2,1,1], [3,3,3,3,2,2,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200 (terms n = 1..147 from Charles R Greathouse IV)

Crossrefs

Cf. A240127.

Programs

Mathematica

f[x_] := x^(1/3); z = 26; ColumnForm[t = Map[Select[IntegerPartitions[#], IntegerQ[f[Total[#^3]]] &] &, Range[z]] ](* shows the partitions *)
t2 = Map[Length[Select[IntegerPartitions[#], IntegerQ[f[Total[#^2]]] &]] &, Range[40]] (* A240128 *) (* Peter J. C. Moses, Apr 01 2014 *)

PARI

a(n)=my(s); forpart(v=n, s+=ispower(sum(i=1, #v, v[i]^3),3)); s \\ Charles R Greathouse IV, Mar 06 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 03 2024