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A344480
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a(n) = Sum_{d|n} d * sigma_d(d), where sigma_k(n) is the sum of the k-th powers of the divisors of n.
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1
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1, 11, 85, 1103, 15631, 284795, 5764809, 134745175, 3486961642, 100097682141, 3138428376733, 107019534806039, 3937376385699303, 155577590686826319, 6568408813691811835, 295152408847835466855, 14063084452067724991027, 708238048886862707907062, 37589973457545958193355621, 2097154000001929438984022793
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OFFSET
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1,2
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COMMENTS
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If p is prime, a(p) = Sum_{d|p} d * sigma_d(d) = 1*(1^1) + p*(1^p + p^p) = 1 + p + p^(p+1).
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LINKS
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EXAMPLE
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a(6) = Sum_{d|6} d * sigma_d(d) = 1*(1^1) + 2*(1^2 + 2^2) + 3*(1^3 + 3^3) + 6*(1^6 + 2^6 + 3^6 + 6^6) = 284795.
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MATHEMATICA
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Table[Sum[k*DivisorSigma[k, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 30}]
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PROG
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(PARI) a(n) = sumdiv(n, d, d*sigma(d, d)); \\ Michel Marcus, May 21 2021
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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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