A339218 Number of partitions of n into prime parts where every part appears at least 2 times.

1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 3, 0, 3, 1, 4, 3, 5, 1, 6, 4, 8, 6, 9, 5, 12, 9, 14, 11, 17, 13, 22, 17, 24, 21, 31, 26, 37, 31, 42, 39, 52, 46, 61, 56, 71, 67, 84, 79, 100, 95, 114, 111, 135, 131, 158, 154, 180, 180, 212, 209, 244, 244, 280, 283, 324, 325, 372, 378, 426, 434, 487

Offset

0,7

Links

Table of n, a(n) for n=0..70.

Index entries for sequences related to partitions

Formula

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

Example

a(10) = 3 because we have [5, 5], [3, 3, 2, 2] and [2, 2, 2, 2, 2].

Mathematica

nmax = 70; CoefficientList[Series[Product[1 + x^(2 Prime[k])/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000040, A000607, A007690, A161077.

Sequence in context: A340502 A055186 A217760 * A263412 A321258 A331510

Adjacent sequences: A339215 A339216 A339217 * A339219 A339220 A339221

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 27 2020

Status

approved