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A348398
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a(n) = Sum_{d|n} sigma_[n/d](d), where sigma_[k](n) is the sum of the k-th powers of the divisors of n.
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0
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1, 4, 5, 13, 7, 32, 9, 54, 42, 78, 13, 299, 15, 204, 395, 647, 19, 1626, 21, 2881, 2565, 2208, 25, 17070, 3158, 8406, 20482, 35607, 31, 116964, 33, 136104, 178529, 131418, 94983, 1112928, 39, 524712, 1596579, 2533908, 43, 7283718, 45, 8405995, 16364934, 8389212, 49, 78586033, 823602, 43423962
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..50.
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EXAMPLE
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a(8) = 54; a(8) = sigma_[8/1](1) + sigma_[8/2](2) + sigma_[8/4](4) + sigma_[8/8](8) = (1^8) + (1^4 + 2^4) + (1^2 + 2^2 + 4^2) + (1^1 + 2^1 + 4^1 + 8^1) = 54.
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MATHEMATICA
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a[n_] := DivisorSum[n, DivisorSigma[n/#, #] &]; Array[a, 50] (* Amiram Eldar, Oct 17 2021 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, sigma(d, n/d)); \\ Michel Marcus, Oct 18 2021
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CROSSREFS
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Cf. A321141.
Sequence in context: A028272 A003969 A326828 * A132140 A102703 A283483
Adjacent sequences: A348395 A348396 A348397 * A348399 A348400 A348401
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KEYWORD
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nonn
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AUTHOR
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Wesley Ivan Hurt, Oct 16 2021
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STATUS
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approved
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