A298603 Number of partitions of n into odd prime parts (including 1).

1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 22, 26, 31, 36, 42, 49, 56, 65, 75, 86, 98, 112, 127, 144, 164, 185, 209, 235, 264, 297, 332, 372, 416, 463, 516, 574, 638, 708, 785, 869, 960, 1061, 1171, 1291, 1421, 1563, 1718, 1886, 2070, 2269, 2484, 2718, 2972, 3247, 3545, 3868, 4216, 4592

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2018

Keywords

• nonn

Comments

Partial sums of A099773.

Examples

			a(6) = 4 because we have [5, 1], [3, 3], [3, 1, 1, 1] and [1, 1, 1, 1, 1, 1].
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000607, A006005, A008578, A034891, A099773, A298604.

Programs

Mathematica

nmax = 62; CoefficientList[Series[1/(1 - x) Product[1/(1 - x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x]

Formula

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