|
Search: id:A085567
|
|
|
| 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. |
|
+0
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
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
"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.
|
|
EXAMPLE
|
a(2)=4 because (1/4)*(1+2+2+3) = 2.
|
|
CROSSREFS
|
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
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Jason Earls (zevi_35711(AT)yahoo.com), Jul 06 2003
|
|
EXTENSIONS
|
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
Added missing terms for a(16)-a(17) and a(20)-a(29) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 21 2008
|
|
|
Search completed in 0.002 seconds
|
