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A294335
Number of compositions (ordered partitions) of n into cubes dividing n.
0
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 2, 1, 1, 1, 1, 345, 1, 1, 1, 1, 1, 1, 1, 1824, 1, 1, 1, 1, 1, 1, 1, 9661, 1, 1, 1, 1, 1, 30, 1, 51284, 1, 1, 1, 1, 1, 1, 1, 272334, 1, 1, 1, 1, 1, 1, 1, 1445995, 1, 1, 1, 1, 1, 1, 1, 7677250, 463, 1, 1, 1, 1
OFFSET
0,9
FORMULA
a(m)=1 when m is cubefree (A004709) and a(m)<>1 when m is not cubefree (A046099). - Michel Marcus, Oct 29 2017
EXAMPLE
a(16) = 11 because 16 has 5 divisors {1, 2, 4, 8, 16} among which 2 are cubes {1, 8} therefore we have [8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 1, 1, 1, 1, 1, 1], [1, 1, 1, 8, 1, 1, 1, 1, 1], [1, 1, 1, 1, 8, 1, 1, 1, 1], [1, 1, 1, 1, 1, 8, 1, 1, 1], [1, 1, 1, 1, 1, 1, 8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 8, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] == 0 && IntegerQ[k^(1/3)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 85}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 28 2017
STATUS
approved