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

Author

Jason Earls, Jul 06 2003

Keywords

• nonn

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

Examples

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

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

Crossrefs

Cf. A050226, A057494, A085829.

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