A309811 (sigma, tau)-superchampion numbers: numbers k for which there is a positive exponent e such that sigma(k)/(k*tau(k)^e) >= sigma(j)/(j*tau(j)^e) for all j >= 1, where tau(k) is the number of divisors of k (A000005) and sigma(k) is their sum (A000203).

1, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 2162160, 4324320, 73513440, 367567200, 6983776800, 160626866400, 321253732800, 9316358251200, 288807105787200, 2021649740510400, 74801040398884800, 224403121196654400, 9200527969062830400, 395622702669701707200

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Jean-Louis Nicolas, Quelques inégalités effectives entre des fonctions arithmétiques usuelles, Functiones et Approximatio, Vol. 39, No. 2 (2008), pp. 315-334. See section 3.

Crossrefs

Cf. A000005, A000203, A002201, A004490.

Sequence in context: A263572 A004490 A224078 * A309233 A135060 A185021

Adjacent sequences: A309808 A309809 A309810 * A309812 A309813 A309814

Keyword

nonn

Author

Amiram Eldar, Aug 25 2019

Status

approved