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A013970
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a(n) = sum of 22nd powers of divisors of n.
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5
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1, 4194305, 31381059610, 17592190238721, 2384185791015626, 131621735227521050, 3909821048582988050, 73786993887028445185, 984770902214992292491, 10000002384185795209930, 81402749386839761113322
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OFFSET
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1,2
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COMMENTS
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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. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sigma(n)
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FORMULA
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G.f.: Sum_{k>=1} k^22*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
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MATHEMATICA
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lst={}; Do[AppendTo[lst, DivisorSigma[22, n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
a[ n_] := DivisorSigma[ 22, n]; (* Michael Somos, Dec 19 2016 *)
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PROG
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(Sage) [sigma(n, 22)for n in range(1, 12)] # Zerinvary Lajos, Jun 04 2009
(PARI) vector(50, n, sigma(n, 22)) \\ G. C. Greubel, Nov 03 2018
(MAGMA) [DivisorSigma(22, n): n in [1..50]]; // G. C. Greubel, Nov 03 2018
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CROSSREFS
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Sequence in context: A017447 A017579 A017707 * A036100 A236946 A258884
Adjacent sequences: A013967 A013968 A013969 * A013971 A013972 A013973
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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