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%I #11 Aug 26 2019 18:43:51
%S 2,116288545977326780410953600,581442729886633902054768000,
%T 7093601304616933605068169600,35468006523084668025340848000,
%U 475271287409334551539567363200,2376356437046672757697836816000,168721307030313765796546413936000,1855934377333451423762010553296000
%N Numbers n > 1 that give record values for f(n) = sigma(n)/(n*log(log(3*d(n)))), where d(n) is the number of divisors of n (A000005) and sigma(n) is their sum (A000203).
%C Nicolas proved that f(n) reaches its maximum at n = 2^3 * (3#)^2 * 5# * 13# * 113# = 8201519488959040182625924708238885435575055666675808000 ~ 8.2 * 10^54 which is the last term of this sequence (prime(n)# = A002110(n) is the n-th primorial).
%H Amiram Eldar, <a href="/A309966/b309966.txt">Table of n, a(n) for n = 1..26</a>
%H Jean-Louis Nicolas, <a href="https://projecteuclid.org/euclid.facm/1229696578">Quelques inégalités effectives entre des fonctions arithmétiques usuelles</a>, Functiones et Approximatio, Vol. 39, No. 2 (2008), pp. 315-334. See Theorem 1.2.
%Y Cf. A000005, A000203, A217660.
%Y Subsequence of A025487.
%K nonn,fini
%O 1,1
%A _Amiram Eldar_, Aug 25 2019