%I
%S 1,1,1,3,7,16,34,70,130,235,445,769,1417,2497,4177,6529,11233,17713,
%T 30673,49033,76233,119433,205833,316713,471945,715881,1026345,1449705,
%U 2296425,3376425,5536425,8128425,11814825,17528745,25242537,34480425,52956201,81509673
%N Number of different nonnegative solutions of equation: x^2  y^2 = k! for 1 <= k <= n.
%F a(n)=sum(k=1..n, A138196(k) )
%t kkk = 1; cc = {1, 1, 1}; Do[w = n!/4; kk = Floor[(DivisorSigma[0, w] + 1)/2]; kkk = kkk + kk; AppendTo[cc, kkk], {n, 4, 54}]; cc
%Y Cf. A138196, A139151, A181892.
%K nonn
%O 1,4
%A _Artur Jasinski_, Mar 31 2012
