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A094947
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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.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
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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)*...
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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)
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CROSSREFS
| Cf. A095001.
Sequence in context: A069866 A125772 A001000 * A092621 A188809 A152449
Adjacent sequences: A094944 A094945 A094946 * A094948 A094949 A094950
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 25 2004
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