A352165 Number of partitions of n into odd prime powers (1 included).

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 26, 31, 37, 44, 52, 61, 71, 83, 97, 112, 130, 150, 173, 199, 228, 261, 298, 340, 386, 439, 497, 563, 637, 718, 809, 910, 1023, 1147, 1286, 1439, 1608, 1796, 2003, 2231, 2483, 2761, 3065, 3401, 3770, 4175, 4619

Offset

0,4

Links

Table of n, a(n) for n=0..55.

Formula

G.f.: Product_{k>=0} 1 / (1 - x^A061345(k)).

Mathematica

nmax = 55; CoefficientList[Series[Product[1/(1 - Boole[(PrimePowerQ[k] || k == 1) && OddQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000961, A023893, A023894, A061345, A099773, A134345, A280151, A352166.

Sequence in context: A034144 A347586 A287997 * A034145 A034146 A287998

Adjacent sequences: A352162 A352163 A352164 * A352166 A352167 A352168

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 06 2022

Status

approved