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Search: id:A085567
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| A085567 |
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Least m such that the average number of divisors of all integers from 1 to m equals n, or 0 if no such number exists. |
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+0
5
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| 1, 4, 15, 42, 121, 336, 930, 2548, 6937, 0, 51322, 0, 379097, 0, 2801205, 56264090, 152941920
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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"In 1838 Lejeune Dirichlet (1805-1859) proved that (1/n)*sum_{r=1..n} #(divisors(r)), the average number of divisors of all integers from 1 to n, approaches ln n + 2gamma - 1 as n increases." -Havil
a(n+1)/a(n) ~ e. - Robert G. Wilson v.
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REFERENCES
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Julian Havil, "Gamma: Exploring Euler's Constant", Princeton University Press, Princeton and Oxford, pp. 112-113, 2003.
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EXAMPLE
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a(2)=4 because (1/4)*(1+2+2+3) = 2.
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CROSSREFS
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Cf. A050226, A057494, A085829.
Sequence in context: A075468 A100503 A085829 this_sequence A075673 A062827 A074448
Adjacent sequences: A085564 A085565 A085566 this_sequence A085568 A085569 A085570
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KEYWORD
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more,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jul 06 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 07 2003
Corrected by Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 28 2003
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