A298604 Number of partitions of n into distinct odd prime parts (including 1).

1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 5, 5, 6, 6, 7, 7, 8, 9, 8, 9, 10, 11, 12, 11, 12, 14, 14, 15, 16, 17, 17, 17, 20, 22, 21, 22, 24, 25, 27, 28, 30, 31, 31, 33, 36, 39, 40, 40, 42, 46, 47, 49, 53, 54, 55, 58, 63, 67, 68, 70, 73, 77, 81, 84

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2018

Keywords

• nonn

Examples

			a(16) = 3 because we have [13, 3], [11, 5] and [7, 5, 3, 1].
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000586, A006005, A008578, A024939, A036497, A298603.

Programs

Mathematica

nmax = 78; CoefficientList[Series[(1 + x) Product[(1 + x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x]

Formula

G.f.: (1 + x)*Product_{k>=2} (1 + x^prime(k)).