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A073706
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a(n) = Sum_{ d divides n } (n/d)^(3d).
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3
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1, 9, 28, 129, 126, 1458, 344, 8705, 20413, 49394, 1332, 1104114, 2198, 2217546, 16305408, 33820673, 4914, 532253187, 6860, 2392632274, 10500716072, 8591716802, 12168, 422182489826, 30517593751, 549760658274, 7625984925160
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{n>=1} -log(1 - (n^3)*x^n)/n = Sum_{n>=1} a(n) x^n/n.
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EXAMPLE
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a(10) = (10/1)^(3*1) +(10/2)^(3*2) +(10/5)^(3*5) +(10/10)^(3*10) = 49394 because positive divisors of 10 are 1, 2, 5, 10.
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MATHEMATICA
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Table[Total[Quotient[n, x = Divisors[n]]^(3*x)], {n, 27}] (* Jayanta Basu, Jul 08 2013 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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