A290370 Number of partitions of n into distinct parts that contain primes to odd powers only (A002035).
1, 0, 1, 1, 0, 2, 1, 2, 3, 2, 4, 4, 3, 7, 5, 8, 9, 9, 12, 12, 14, 18, 18, 22, 27, 25, 34, 34, 39, 47, 49, 57, 67, 67, 83, 88, 96, 115, 119, 139, 154, 165, 190, 206, 224, 259, 273, 311, 341, 367, 415, 447, 490, 550, 588, 654, 720, 771, 862, 928, 1013, 1121, 1204, 1324, 1448, 1554, 1716, 1850, 2008, 2203, 2366
Offset: 0
Keywords
Examples
a(8) = 3 because we have [8], [6, 2] and [5, 3].
Programs
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Mathematica
nmax = 70; CoefficientList[Series[Product[1 + Boole[And @@ OddQ /@ FactorInteger[k][[All, 2]]] x^k, {k, 2, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=1} (1 + x^A002035(k)).