A352166 Number of partitions of n into distinct odd prime powers (1 included).
1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 4, 5, 6, 6, 6, 7, 8, 9, 9, 10, 12, 12, 13, 14, 16, 17, 17, 19, 21, 23, 23, 25, 28, 30, 31, 33, 37, 38, 40, 43, 47, 50, 52, 55, 60, 64, 66, 70, 76, 81, 83, 89, 96, 101, 105, 110, 119, 125, 130, 138, 147, 155, 161
Offset: 0
Keywords
Programs
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Mathematica
nmax = 70; CoefficientList[Series[Product[(1 + Boole[(PrimePowerQ[k] || k == 1) && OddQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=0} (1 + x^A061345(k)).