A294333 Number of partitions of n into cubes dividing n.

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..6640

Index entries for sequences related to partitions

Index entries for sequences related to sums of cubes

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

Cf. A018818, A003108, A004709, A030078, A061704, A284345.

Sequence in context: A355936 A326976 A117358 * A321125 A205617 A359888

Adjacent sequences: A294330 A294331 A294332 * A294334 A294335 A294336

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 28 2017

Status

approved