A100854 Least number of positive cubes that sum to n^2.

1, 4, 2, 2, 4, 3, 7, 1, 3, 4, 6, 4, 5, 6, 3, 4, 4, 5, 5, 6, 4, 4, 4, 2, 5, 5, 1, 4, 5, 4, 4, 2, 4, 5, 4, 4, 4, 6, 4, 4, 5, 4, 6, 5, 4, 6, 6, 3, 4, 5, 5, 6, 3, 4, 4, 5, 5, 5, 3, 4, 5, 4, 4, 1, 4, 5, 5, 4, 4, 6, 3, 3, 5, 6, 5, 4, 4, 3, 5, 4, 2, 5, 5, 3, 5, 5, 3, 6, 5, 3, 4, 6, 5, 5, 4, 3, 5, 2, 4, 3

Offset: 1

Author

Giovanni Teofilatto, Jan 08 2005

Keywords

• easy
• nonn

Examples

			a(2)=4 because 4=1+1+1+1;
a(3)=2 because 9=1+8;
a(4)=2 because 16=8+8.
		

Crossrefs

Cf. A002376 (least number of positive cubes needed to represent n).

Programs

Mathematica

nn=100^2; cnt=Table[10, {nn}]; maxN=Floor[nn^(1/3)]; Do[v={a, b, c, d, e, f, g, h, i}; n=Plus@@(v^3); If[n>0 && n<=nn, cnt[[n]]=Min[cnt[[n]], 9-Count[v, 0]]], {a, 0, maxN}, {b, a, maxN}, {c, b, maxN}, {d, c, maxN}, {e, d, maxN}, {f, e, maxN}, {g, f, maxN}, {h, f, maxN}, {i, h, maxN}]; Table[cnt[[n^2]], {n, 100}] (T. D. Noe)

Formula

a(n) = A002376(n^2). - R. J. Mathar, May 06 2016

Extensions

Corrected and extended by T. D. Noe, Jan 10 2005