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%I #7 Mar 15 2017 20:26:57
%S 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,
%T 10,12,12,13,14,14,17,16,19,19,21,22,23,25,27,27,30,30,34,35,37,40,41,
%U 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
%N Number of partitions of n into primes of form x^2 + y^2 (A002313).
%C Number of partitions of n into primes congruent to 1 or 2 mod 4.
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A002313(k)).
%e a(10) = 2 because we have [5, 5] and [2, 2, 2, 2, 2].
%t nmax = 82; CoefficientList[Series[Product[1/(1 - Boole[SquaresR[2, k] != 0 && PrimeQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%o (PARI) Vec(prod(k=1, 82, (1/(1 - (isprime(k) && k%4<3)*x^k))) + O(x^83)) \\ _Indranil Ghosh_, Mar 15 2017
%Y Cf. A000607, A002313, A024941, A281273.
%K nonn
%O 0,11
%A _Ilya Gutkovskiy_, Feb 25 2017
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