A309966 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).

2, 116288545977326780410953600, 581442729886633902054768000, 7093601304616933605068169600, 35468006523084668025340848000, 475271287409334551539567363200, 2376356437046672757697836816000, 168721307030313765796546413936000, 1855934377333451423762010553296000

Offset: 1

Author

Amiram Eldar, Aug 25 2019

Keywords

• nonn
• fini

Comments

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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..26
• Jean-Louis Nicolas, Quelques inégalités effectives entre des fonctions arithmétiques usuelles, Functiones et Approximatio, Vol. 39, No. 2 (2008), pp. 315-334. See Theorem 1.2.

Crossrefs

Cf. A000005, A000203, A217660.

Subsequence of A025487.