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A085567
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.
5
1, 4, 15, 42, 121, 336, 930, 2548, 6937, 0, 51322, 0, 379097, 0, 2801205, 0, 20698345, 56264090, 152941920, 0, 0, 0, 8350344420, 0, 61701166395, 0, 455913379395, 1239301050694, 3368769533660, 0, 24892027072619, 0, 183928584450999, 0, 0, 0
OFFSET
1,2
COMMENTS
"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
REFERENCES
Julian Havil, "Gamma: Exploring Euler's Constant", Princeton University Press, Princeton and Oxford, pp. 112-113, 2003.
LINKS
EXAMPLE
a(2) = 4 because (1/4)*(1+2+2+3) = 2.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Jul 06 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jul 07 2003
Corrected by Rick L. Shepherd, Aug 28 2003
Missing terms a(16)-a(17) and a(20)-a(29) added by Donovan Johnson, Dec 21 2008
a(30)-a(36) from Donovan Johnson, Jul 20 2011
STATUS
approved