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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.

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

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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 * A213498 A294259 A240359

Adjacent sequences: A085564 A085565 A085566 * A085568 A085569 A085570

KEYWORD