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Search: id:A013964
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| A013964 |
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sigma_16(n), the sum of the 16th powers of the divisors of n. |
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+0
3
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| 1, 65537, 43046722, 4295032833, 152587890626, 2821153019714, 33232930569602, 281479271743489, 1853020231898563, 10000152587956162, 45949729863572162, 184887084343023426, 665416609183179842
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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^16*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: A013961 A013962 A013963 this_sequence A013965 A013966 A013967
Sequence in context: A070816 A133864 A017695 this_sequence A036094 A133865 A096555
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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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