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Search: id:A159604
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| A159604 |
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G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(n,k)*x^k ]^n/n ). |
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+0
1
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| 1, 1, 6, 43, 856, 10744, 608375, 14284223, 551011548, 19119025101, 874788949035, 37896009869060, 20683158266928833, 1799893777863733707, 93147805938921355288, 3757831283217050847983, 180287028377782585130749
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Define sigma(n,k) = Sum_{d|n} d^k.
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EXAMPLE
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G.f.: A(x) = 1 + x + 6*x^2 + 43*x^3 + 856*x^4 + 10744*x^5 +...
log(A(x)) = Sum_{n>=1} [sigma(n)*x + sigma(n,2)*x^2 + sigma(n,3)*x^3 +...]^n/n.
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, sigma(m, k)*x^k+x*O(x^n))^m/m))); polcoeff(A, n)}
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CROSSREFS
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Cf. variants: A159595, A156217.
Sequence in context: A146966 A090010 A062266 this_sequence A090338 A090339 A078810
Adjacent sequences: A159601 A159602 A159603 this_sequence A159605 A159606 A159607
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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), May 16 2009
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