OFFSET
0,3
COMMENTS
Number of partitions of n into prime parts of 2 kinds.
Self-convolution of A000607.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^prime(k))^2.
log(a(n)) ~ 2*Pi*sqrt(2*n/(3*log(n/2))). - Vaclav Kotesovec, Jan 12 2021
EXAMPLE
a(5) = 6 because we have [5a], [5b], [3a, 2a], [3a, 2b], [3b, 2a] and [3b, 2b].
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[1/(1 - x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 19 2018
STATUS
approved