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A013969
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sigma_21(n), the sum of the 21st powers of the divisors of n.
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2
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1, 2097153, 10460353204, 4398048608257, 476837158203126, 21936961102828212, 558545864083284008, 9223376434903384065, 109418989141972712413, 1000000476837160300278, 7400249944258160101212, 46005141850728850805428
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| G.f. sum(k>=1, k^21*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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MATHEMATICA
| lst={}; Do[AppendTo[lst, DivisorSigma[21, n]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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PROG
| (Other) sage: [sigma(n, 21)for n in xrange(1, 13)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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CROSSREFS
| Sequence in context: A017706 A010809 A017705 * A036099 A203786 A043630
Adjacent sequences: A013966 A013967 A013968 * A013970 A013971 A013972
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KEYWORD
| nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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