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Search: id:A095895
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| A095895 |
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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. |
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1
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| 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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.
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PROGRAM
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(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)
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CROSSREFS
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Cf. A094947, A007947.
Sequence in context: A064450 A130623 A072847 this_sequence A051934 A153915 A093705
Adjacent sequences: A095892 A095893 A095894 this_sequence A095896 A095897 A095898
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 11 2004
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