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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).
1
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
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
Subsequence of A025487.
Sequence in context: A257229 A176944 A068138 * A082566 A273400 A371468
KEYWORD
nonn,fini
AUTHOR
Amiram Eldar, Aug 25 2019
STATUS
approved