A094947 G.f.: A(x) = Product_{n>=1} 1/(1 - A007947(n)*x^n)^(1/n), where A007947(n) is the product of the distinct prime factors of n.

1, 1, 2, 3, 5, 7, 13, 17, 27, 39, 61, 82, 136, 179, 275, 398, 584, 796, 1251, 1668, 2516, 3577, 5198, 7100, 10931, 14797, 21738, 30929, 44622, 61209, 93557, 126219, 184593, 262621, 376923, 521670, 785414, 1066281, 1550829, 2211872, 3173795, 4381455

Offset

0,3

Comments

Sequence consists entirely of integers, even though the g.f. is obtained by the infinite product of the n-th roots of 1/(1 - A007947(n)*x^n).

Limit of a(n)/a(n+1) = (1/3)^(1/3) as n grows.

Links

Table of n, a(n) for n=0..41.

Example

1/A(x) = (1-x)*(1-2x^2)^(1/2)*(1-3x^3)^(1/3)*(1-2x^4)^(1/4)*(1-5x^5)^(1/5)*...

Prog

(PARI) a(n)=polcoeff(prod(k=1, n, 1/(1-prod(i=1, omega(k), factor(k)[i, 1])*x^k+x*O(x^n))^(1/k)), n)

Crossrefs

Cf. A095001.

Sequence in context: A125772 A233282 A001000 * A231474 A092621 A188809

Adjacent sequences: A094944 A094945 A094946 * A094948 A094949 A094950

Keyword

nonn

Author

Paul D. Hanna, May 25 2004

Status

approved