A309811 - OEIS

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).

%I #27 Aug 26 2019 12:56:09

%S 1,2,6,12,60,120,360,2520,5040,55440,720720,2162160,4324320,73513440,

%T 367567200,6983776800,160626866400,321253732800,9316358251200,

%U 288807105787200,2021649740510400,74801040398884800,224403121196654400,9200527969062830400,395622702669701707200

%N (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).

%H Jean-Louis Nicolas, <a href="https://projecteuclid.org/euclid.facm/1229696578">Quelques inégalités effectives entre des fonctions arithmétiques usuelles</a>, Functiones et Approximatio, Vol. 39, No. 2 (2008), pp. 315-334. See section 3.

%Y Cf. A000005, A000203, A002201, A004490.

%K nonn

%O 1,2

%A _Amiram Eldar_, Aug 25 2019