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
Keywords
Programs
-
Mathematica
nmax = 55; CoefficientList[Series[Product[1/(1 - Boole[(PrimePowerQ[k] || k == 1) && OddQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=0} 1 / (1 - x^A061345(k)).