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Search: id:A051377
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| A051377 |
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Sum of exponential divisors (or e-divisors) of n. |
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+0
11
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| 1, 2, 3, 6, 5, 6, 7, 10, 12, 10, 11, 18, 13, 14, 15, 22, 17, 24, 19, 30, 21, 22, 23, 30, 30, 26, 30, 42, 29, 30, 31, 34, 33, 34, 35, 72, 37, 38, 39, 50, 41, 42, 43, 66, 60, 46, 47, 66, 56, 60, 51, 78, 53, 60, 55, 70, 57, 58, 59, 90, 61, 62, 84, 78, 65, 66, 67, 102, 69, 70, 71
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The e-divisors (or exponential divisors) of x=Product p(i)^r(i) are all numbers of the form Product p(i)^s(i) where s(i) divides r(i) for all i.
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REFERENCES
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Fabrykowski, J. and Subbarao, M. V., The maximal order and the average order of multiplicative function sigma^(e)(n), in Theorie des nombres (Quebec, PQ, 1987), 201-206, de Gruyter, Berlin, 1989.
Petermann, Y.-F. S. and Wu, J., On the sum of exponential divisors of an integer, Acta Math. Hungar. 77 (1997), 159-175.
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LINKS
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Eric Weisstein's World of Mathematics, Definition
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FORMULA
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Multiplicative with a(p^e) = Sum_{d|e} p^d. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 23 2002
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EXAMPLE
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a(8)=10 because 2 and 2^3 are e-divisors of 8, and 2+2^3=10.
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CROSSREFS
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Cf. A051378, A049419.
Adjacent sequences: A051374 A051375 A051376 this_sequence A051378 A051379 A051380
Sequence in context: A093783 A096861 A118738 this_sequence A057723 A142151 A003968
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), May 29 2000
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