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A198301
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G.f.: exp( Sum_{n>=1} (x^n/n) * Sum_{d|n} d*sigma(n/d,d) ).
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1
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1, 1, 3, 5, 12, 18, 42, 62, 131, 206, 398, 610, 1203, 1810, 3358, 5260, 9471, 14518, 26182, 39906, 70320, 108849, 187251, 287525, 497288, 758860, 1286936, 1986352, 3330677, 5102712, 8560107, 13070327, 21685731, 33328561, 54744685, 83792111, 137817745, 210223967
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OFFSET
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0,3
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COMMENTS
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Here sigma(n,k) is the sum of the k-th powers of the divisors of n.
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LINKS
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FORMULA
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G.f.: exp( Sum_{n>=1} Sum_{k>=1} sigma(n,k) * x^(n*k)/n ).
Logarithmic derivative yields A198302.
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 12*x^4 + 18*x^5 + 42*x^6 + 62*x^7 +...
where the logarithm begins:
log(A(x)) = x + 5*x^2/2 + 7*x^3/3 + 21*x^4/4 + 11*x^5/5 + 65*x^6/6 + 15*x^7/7 + 133*x^8/8 + 106*x^9/9 +...+ A198302(n)*x^n/n +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, d*sigma(m/d, d))*x^m/m)+x*O(x^n)), n)}
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sum(k=1, n\m, sigma(m, k)*x^(m*k)/m)+x*O(x^n))), n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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