A308618 Cubefree superabundant numbers: cubefree numbers (A004709) k such that sigma(k)/k > sigma(j)/j for all cubefree numbers j < k.

1, 2, 4, 6, 12, 30, 36, 60, 180, 420, 1260, 4620, 6300, 13860, 69300, 180180, 900900, 3063060, 15315300, 58198140, 290990700, 1338557220, 2036934900, 6692786100, 38818159380, 46849502700, 194090796900, 1358635578300, 6016814703900, 42117702927300, 222622144044300

Offset: 1

Author

Amiram Eldar, Aug 21 2019

Keywords

• nonn

Comments

Erdős and Nicolas named these numbers "nombres sans cube superabondants".

All the terms are either primorials (A002110) or products of two primorials.

Also numbers m such that A073185(m)/m > A073185(k)/k for all k < m. - Amiram Eldar, Oct 08 2022

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1307
• Paul Erdős and Jean-Louis Nicolas, Répartition des nombres superabondants", Bulletin de la Société Mathématique de France, Vol. 103 (1975), pp. 65-90. See section 5, p. 83.

Crossrefs

Cf. A000203, A002110, A004394, A004709, A073185.

Subsequence of A025487 and A220423.

Programs

Mathematica

cubeFreeQ[n_] := Max @ FactorInteger[n][[;;, 2]] < 3; s = {}; rm = 0; Do[If[ !cubeFreeQ[n], Continue[]]; r = DivisorSigma[1, n]/n; If[r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^6}]; s