OFFSET
0,17
FORMULA
G.f.: Product_{k>=1} (1 + x^(2*k^3) / (1 - x^(k^3))).
EXAMPLE
a(24) = 3 because we have [8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 95; CoefficientList[Series[Product[1 + x^(2 k^3)/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x]
Table[Length[Select[IntegerPartitions[n], AllTrue[Surd[#, 3], IntegerQ] && Min[ Tally[ #][[All, 2]]]>1&]], {n, 0, 100}] (* Requires Mathematica version 10 or later *) (* The program takes a long time to run. *) (* Harvey P. Dale, May 03 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 27 2020
STATUS
approved