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A356042
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a(n) = Sum_{k=1..n} sigma_2(k) * floor(n/k).
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2
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1, 7, 18, 45, 72, 138, 189, 301, 403, 565, 688, 985, 1156, 1462, 1759, 2212, 2503, 3115, 3478, 4207, 4768, 5506, 6037, 7269, 7947, 8973, 9895, 11272, 12115, 13897, 14860, 16678, 18031, 19777, 21154, 23908, 25279, 27457, 29338, 32362, 34045, 37411, 39262, 42583
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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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a(n) = Sum_{k=1..n} Sum_{d|k} d^2 * tau(k/d).
G.f.: (1/(1-x)) * Sum_{k>=1} sigma_2(k) * x^k/(1 - x^k).
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MATHEMATICA
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Table[Sum[DivisorSigma[2, k]*Floor[n/k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Aug 07 2022 *)
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PROG
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(PARI) a(n) = sum(k=1, n, sigma(k, 2)*(n\k));
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^2*numdiv(k/d)));
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, 2)*x^k/(1-x^k))/(1-x))
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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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