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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

%I #10 Mar 20 2013 18:18:53

%S 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

%N 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.

%C See comments, references, links and crossrefs in A067698.

%H G. Caveney, J.-L. Nicolas, and J. Sondow, <a href="http://www.integers-ejcnt.org/l33/l33.pdf">Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis</a>, Integers 11 (2011), #A33; see Table 1 and Lemma 11.

%H G. Caveney, J.-L. Nicolas and J. Sondow, <a href="http://arxiv.org/abs/1112.6010">On SA, CA, and GA numbers</a>, Ramanujan J., 29 (2012), 359-384.

%e 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.

%Y Cf. A067698.

%K nonn

%O 1,5

%A Geoffrey Caveney, Jean-Louis Nicolas, and _Jonathan Sondow_, Sep 29 2011