A309968 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).

2, 74801040398884800, 224403121196654400, 3066842656354276800, 6133685312708553600, 9200527969062830400, 18401055938125660800, 131874234223233902400, 263748468446467804800, 395622702669701707200, 791245405339403414400, 6198089008491993412800, 12396178016983986825600

Offset

1,1

Comments

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..68

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, A073004, A073226, A217660.

Subsequence of A025487.

Sequence in context: A257229 A176944 A068138 * A082566 A273400 A371468

Adjacent sequences: A309965 A309966 A309967 * A309969 A309970 A309971

Keyword

nonn,fini

Author

Amiram Eldar, Aug 25 2019

Status

approved