A095895 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.

1, 1, 2, 3, 6, 8, 22, 27, 62, 107, 230, 309, 942, 1194, 2829, 5489, 11153, 15922, 48863, 64439, 154697, 307045, 615602, 910291, 2826566, 3883346, 8840108, 18696403, 36496897, 55654425, 174825676, 239374320, 537938704, 1197382791, 2267244673

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..34.

Prog

(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)

Crossrefs

Cf. A094947, A007947.

Sequence in context: A072847 A274371 A339589 * A051934 A153915 A355581

Adjacent sequences: A095892 A095893 A095894 * A095896 A095897 A095898

Keyword

nonn

Author

Paul D. Hanna, Jun 11 2004

Status

approved