A282970 Number of partitions of n into primes of form x^2 + y^2 (A002313).

1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 12, 12, 13, 14, 14, 17, 16, 19, 19, 21, 22, 23, 25, 27, 27, 30, 30, 34, 35, 37, 40, 41, 45, 46, 50, 52, 55, 58, 60, 65, 67, 71, 75, 78, 84, 86, 92, 97, 100, 108, 110, 118, 123, 127, 137, 139, 150, 154, 162

Offset: 0

Author

Ilya Gutkovskiy, Feb 25 2017

Keywords

• nonn

Comments

Number of partitions of n into primes congruent to 1 or 2 mod 4.

Examples

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

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000607, A002313, A024941, A281273.

Programs

Mathematica

nmax = 82; CoefficientList[Series[Product[1/(1 - Boole[SquaresR[2, k] != 0 && PrimeQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

PARI

Vec(prod(k=1, 82, (1/(1 - (isprime(k) && k%4<3)*x^k))) + O(x^83)) \\ Indranil Ghosh, Mar 15 2017

Formula

G.f.: Product_{k>=1} 1/(1 - x^A002313(k)).