A196229 Smallest prime factor p of r = A067698(n) such that sigma(r/p)/((r/p)*log(log(r/p))) > sigma(r)/(r*log(log(r))), where sigma(k) = sum of divisors of k; or 1 if no such p.

1, 1, 1, 1, 2, 2, 3, 2, 2, 2, 3, 5, 3, 3, 2, 3, 5, 3, 7, 2, 5, 5, 5, 3, 7, 7, 2

Offset

1,5

Comments

See comments, references, links and crossrefs in A067698.

Links

Table of n, a(n) for n=1..27.

G. Caveney, J.-L. Nicolas, and J. Sondow, Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis, Integers 11 (2011), #A33; see Table 1 and Lemma 11.

G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Ramanujan J., 29 (2012), 359-384.

Example

A067698(5) = 6 and sigma(6/2)/((6/2)*log(log(6/2))) = 14.17... > 3.42... = sigma(6)/(6*log(log(6))), so a(5) = 2.

Crossrefs

Cf. A067698.

Sequence in context: A300225 A060244 A072814 * A191302 A161189 A328162

Adjacent sequences: A196226 A196227 A196228 * A196230 A196231 A196232

Keyword

nonn

Author

Geoffrey Caveney, Jean-Louis Nicolas, and Jonathan Sondow, Sep 29 2011

Status

approved