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

Author

Ilya Gutkovskiy, Jul 28 2017

Keywords

• nonn

Examples

			a(8) = 3 because we have [8], [6, 2] and [5, 3].
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A002035, A290369.

Programs

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)).