OFFSET
0,3
FORMULA
EXAMPLE
For n = 4 we have:
--------------------------------
Partitions Sum of parts
. which are cubes
--------------------------------
4 ................... 0
3 + 1 ............... 1
2 + 2 ............... 0
2 + 1 + 1 ........... 2
1 + 1 + 1 + 1 ....... 4
--------------------------------
Total ............... 7
So a(4) = 7.
MATHEMATICA
nmax = 45; CoefficientList[Series[Sum[k^3 x^(k^3)/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[DivisorSum[k, # &, IntegerQ[#^(1/3)] &] PartitionsP[n - k], {k, 1, n}], {n, 0, 45}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 06 2021
STATUS
approved