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%I #27 May 05 2018 11:45:16
%S 2,4,16,36,400,1296,1521,52441
%N Numbers n such that A015128(n)/2 is prime.
%C Next term, if it exists, is greater than 4000000. - _Vaclav Kotesovec_, updated Apr 12 2017
%C The values of a(n) are the squares of these integers for 1 < n < 9: 2, 4, 6, 20, 36, 39, 229. Squares also appear in the sequence of numbers k such that A015128(k)/2 is semiprime. - _Altug Alkan_, Dec 16 2015
%e 4 is a term because A015128(4)/2 = 14/2 = 7 is prime.
%t Select[Range[2000], PrimeQ[Sum[PartitionsP[#-k]*PartitionsQ[k], {k, 0, #}]/2] &]
%o (PARI) a015128(n) = polcoeff(exp(sum(m=1, n\2+1, 2*x^(2*m-1)/(1-x^(2*m-1)+x*O(x^n))/(2*m-1))), n);
%o for(n=1, 1e3, if(ispseudoprime(a015128(n)/2), print1(n, ", "))) \\ _Altug Alkan_, Dec 16 2015
%Y Cf. A014968, A015128, A035359, A046063, A299961.
%K nonn,more,hard
%O 1,1
%A _Vaclav Kotesovec_, Dec 16 2015