A309875 Cubefree colossally superabundant numbers: cubefree numbers (A004709) k for which there is a positive exponent epsilon such that sigma(k)/k^{1 + epsilon} >= sigma(j)/j^{1 + epsilon} for all cubefree j > 1, so that k attains the maximum value of sigma(k)/k^{1 + epsilon} over the cubefree numbers.

2, 6, 12, 60, 180, 1260, 13860, 180180, 900900, 15315300, 290990700, 6692786100, 194090796900, 6016814703900, 42117702927300, 1558355008310100, 63892555340714100, 2747379879650706300, 129126854343583196100, 6843723280209909393300, 403779673532384654204700

Offset: 1

Author

Amiram Eldar, Aug 21 2019

Keywords

• nonn

Comments

This sequence is formed by the largest cubefree divisors (A007948) of the colossally superabundant numbers (A004490).

Links

• 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, A004490, A004709, A007948.

Subsequence of A025487, A220423 and A308618.