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A023887
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sigma_n(n): sum of n-th powers of divisors of n.
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5
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1, 5, 28, 273, 3126, 47450, 823544, 16843009, 387440173, 10009766650, 285311670612, 8918294543346, 302875106592254, 11112685048647250, 437893920912786408, 18447025552981295105, 827240261886336764178
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 38.
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LINKS
| N. Hobson, Table of n, a(n) for n = 1..100
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FORMULA
| G.f.: Sum_{n>0} (n*x)^n/(1-(n*x)^n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 27 2002
If the canonical prime factorization of n > 1 is the product of p^e(p) then sigma_n(n) = Product_p ((p^(n*(e(p)+1)))-1)/(p^n-1). - Nick Hobson Nov 25 2006
sigma_n(n) is odd if and only if n is a square or twice a square. - Nick Hobson Nov 25 2006
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EXAMPLE
| The divisors of 6 are 1, 2, 3 and 6, so a(6) = 1^6 + 2^6 + 3^6 + 6^6 = 47450.
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MATHEMATICA
| Table[DivisorSigma[n, n], {n, 1, 50}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 26 2009]
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PROG
| (PARI) a(n) = if(n<1, 0, sigma(n, n)) - Nick Hobson Nov 25 2006
(Maxima) makelist(divsum(n, n), n, 1, 20); [Emanuele Munarini, Mar 26 2011]
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CROSSREFS
| Cf. A000203, A001157-A001160, A013954-A013972.
Sequence in context: A116977 A163694 A062796 * A171187 A057792 A174464
Adjacent sequences: A023884 A023885 A023886 * A023888 A023889 A023890
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 25 2006
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