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A294333
Number of partitions of n into cubes dividing n.
2
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 1, 8, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 11, 4, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 14, 1
OFFSET
0,9
FORMULA
a(n) = 1 if n is a cubefree.
a(n) = 2 if n is a cube of prime.
EXAMPLE
a(8) = 2 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are cubes {1, 8} therefore we have [8] and [1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] == 0 && IntegerQ[k^(1/3)]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 105}]
PROG
(PARI)
cubes_dividing(n) = select(d -> ispower(d, 3), divisors(n));
partitions_into(n, parts, from=1) = if(!n, 1, my(k = #parts, s=0); for(i=from, k, if(parts[i]<=n, s += partitions_into(n-parts[i], parts, i))); (s));
A294333(n) = if(n<2, 1, partitions_into(n, vecsort(cubes_dividing(n), , 4))); \\ Antti Karttunen, Jul 21 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 28 2017
STATUS
approved