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

0,4

Comments

Partial sums of A099773.

Links

Table of n, a(n) for n=0..62.

Index entries for related partition-counting sequences

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A088567 A029014 A304631 * A134345 A112193 A014215

Adjacent sequences: A298600 A298601 A298602 * A298604 A298605 A298606

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2018

Status

approved