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A352165
Number of partitions of n into odd prime powers (1 included).
1
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
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]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 06 2022
STATUS
approved