|
| |
|
|
A197639
|
|
GA2 numbers: n with G(n) >= G(a*n) for all integers a > 0, where G(k) = sigma(k)/(k*log(log(k))) and sigma(k) = sum of divisors of k.
|
|
3
|
|
|
|
3, 4, 5, 6, 8, 10, 12, 18, 24, 36, 48, 60, 72, 120, 180, 240, 360, 2520, 5040
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Subsequence of A067698.
A member > 5040 exists iff the Riemann Hypothesis is false, in which case the sequence is infinite. In any case, 3 and 5 are the only odd members. (See Sections 1 and 4 of "On SA, CA, and GA numbers".)
|
|
|
REFERENCES
|
G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Arxiv preprint arXiv:1112.6010, 2011. - From N. J. A. Sloane, Apr 14 2012
|
|
|
LINKS
|
Table of n, a(n) for n=1..19.
G. Caveney, J.-L. Nicolas, and J. Sondow, Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis, Integers 11 (2011), article A33.
G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Ramanujan J., 29 (2012), 359-384.
|
|
|
CROSSREFS
|
Cf. A000203, A067698, A197638, A201557.
Sequence in context: A180646 A062514 A065875 * A167057 A100585 A023367
Adjacent sequences: A197636 A197637 A197638 * A197640 A197641 A197642
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Geoffrey Caveney, Jean-Louis Nicolas, and Jonathan Sondow, Dec 02 2011
|
|
|
STATUS
|
approved
|
| |
|
|
