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.

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

Donovan Johnson, Table of n, a(n) for n = 1..40

Example

a(2) = 4 because (1/4)*(1+2+2+3) = 2.

Crossrefs

Cf. A050226, A057494, A085829.

Sequence in context: A075468 A100503 A085829 * A187928 A213498 A294259

Adjacent sequences: A085564 A085565 A085566 * A085568 A085569 A085570

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