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%I #5 Mar 30 2012 18:36:40
%S 1,1,2,3,6,8,22,27,62,107,230,309,942,1194,2829,5489,11153,15922,
%T 48863,64439,154697,307045,615602,910291,2826566,3883346,8840108,
%U 18696403,36496897,55654425,174825676,239374320,537938704,1197382791,2267244673
%N G.f.: A(x) = Product_{n>=1} 1/(1 - n*A007947(n)*x^n)^(1/n^2), where A007947(n) is the product of the distinct prime factors of n.
%C In general the smallest positive integers b(n) that produce an integer sequence from the g.f.: Product_{n>=1} (1 - b(n)*x^n)^(1/n^m) is given by b(n) = n^(m-1)*A007947(n), where A007947(n) is the product of the distinct prime factors of n and m is any positive integer.
%o (PARI) a(n)=polcoeff(prod(k=1,n,1/(1-k*prod(i=1,omega(k),factor(k)[i,1])*x^k+x*O (x^n))^(1/k^2)),n)
%Y Cf. A094947, A007947.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 11 2004