A281449 Expansion of Sum_{k>=1} x^(prime(k)^2)/(1 - x^(prime(k)^2)) / Product_{k>=1} (1 - x^(prime(k)^2)).

0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 3, 2, 0, 0, 4, 3, 2, 0, 5, 4, 3, 0, 6, 6, 4, 3, 7, 8, 5, 4, 8, 10, 8, 5, 13, 12, 10, 6, 15, 14, 12, 10, 17, 21, 14, 12, 19, 25, 18, 14, 25, 29, 27, 16, 28, 33, 33, 21, 31, 42, 38, 31, 34, 47, 43, 38, 41, 52, 54, 43, 53, 57, 62, 51, 62, 67, 69, 64, 68, 82, 76, 74, 78, 94, 89, 82, 93

Offset: 1

Author

Ilya Gutkovskiy, Jan 27 2017

Keywords

• nonn

Comments

Total number of parts in all partitions of n into squares of primes (A001248).

Convolution of A056170 and A090677.

Examples

			a(25) = 6 because we have [25], [9, 4, 4, 4, 4] and 1 + 5 = 6.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A001248, A056170, A084993, A090677, A281541.

Programs

Mathematica

nmax = 88; Rest[CoefficientList[Series[Sum[x^Prime[k]^2/(1 - x^Prime[k]^2), {k, 1, nmax}]/Product[1 - x^Prime[k]^2, {k, 1, nmax}], {x, 0, nmax}], x]]

Formula

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