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Search: id:A017665
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| A017665 |
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Numerator of sum of reciprocals of divisors of n. |
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+0
76
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| 1, 3, 4, 7, 6, 2, 8, 15, 13, 9, 12, 7, 14, 12, 8, 31, 18, 13, 20, 21, 32, 18, 24, 5, 31, 21, 40, 2, 30, 12, 32, 63, 16, 27, 48, 91, 38, 30, 56, 9, 42, 16, 44, 21, 26, 36, 48, 31, 57, 93, 24, 49, 54, 20, 72, 15, 80, 45, 60, 14, 62, 48, 104, 127, 84, 24, 68, 63, 32, 72, 72, 65, 74, 57
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OFFSET
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1,2
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COMMENT
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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.
Numerators of coefficients in expansion of Sum_{n >= 1} x^n/(n*(1-x^n)) = Sum_{n >= 1} log(1/(1-x^n).
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 162, #16, (6), 4th formula.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Abundancy
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FORMULA
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sigma(n)/gcd(n, sigma(n)) - Jon Perry (perry(AT)globalnet.co.uk), Jun 29 2003
Dirichlet generating function: zeta(s)*zeta(s+1) [for fraction A017665/A017666]. - Franklin T. Adams-Watters, Sep 11 2005.
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EXAMPLE
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1, 3/2, 4/3, 7/4, 6/5, 2, 8/7, 15/8, 13/9, 9/5, 12/11, 7/3, 14/13, 12/7, 8/5, 31/16, ...
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MAPLE
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with(numtheory): seq(numer(sigma(n)/n), n=1..74) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2008
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CROSSREFS
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Cf. A017666.
Sequence in context: A134688 A077650 A105853 this_sequence A105852 A067342 A105827
Adjacent sequences: A017662 A017663 A017664 this_sequence A017666 A017667 A017668
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KEYWORD
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nonn,frac,nice
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AUTHOR
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njas
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