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%I #13 Aug 26 2019 16:32:48
%S 2,74801040398884800,224403121196654400,3066842656354276800,
%T 6133685312708553600,9200527969062830400,18401055938125660800,
%U 131874234223233902400,263748468446467804800,395622702669701707200,791245405339403414400,6198089008491993412800,12396178016983986825600
%N Numbers n > 1 that give record values for f(n) = sigma(n)/n - e^gamma * log(log(e*d(n))) - e^gamma * log(log(log(e^e * 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 = 2^7 * (3#)^4 * 5# * (7#)^2 * 19# * 47# * 277# * 45439# ~ 8.0244105... * 10^19786 which is the last term of this sequence (prime(n)# = A002110(n) is the n-th primorial).
%H Amiram Eldar, <a href="/A309968/b309968.txt">Table of n, a(n) for n = 1..68</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, A073004, A073226, A217660.
%Y Subsequence of A025487.
%K nonn,fini
%O 1,1
%A _Amiram Eldar_, Aug 25 2019