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Search: id:A013956
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| A013956 |
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sigma_8(n), the sum of the 8th powers of the divisors of n. |
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+0
4
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| 1, 257, 6562, 65793, 390626, 1686434, 5764802, 16843009, 43053283, 100390882, 214358882, 431733666, 815730722, 1481554114, 2563287812, 4311810305, 6975757442, 11064693731, 16983563042, 25700456418
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OFFSET
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1,2
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COMMENT
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If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.
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FORMULA
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G.f. sum(k>=1, k^8*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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CROSSREFS
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Adjacent sequences: A013953 A013954 A013955 this_sequence A013957 A013958 A013959
Sequence in context: A125648 A034682 A017679 this_sequence A036086 A000542 A023877
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KEYWORD
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nonn,mult
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AUTHOR
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njas
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