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

Author

Amiram Eldar, Aug 25 2019

Keywords

• nonn

Links

• 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.