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

1,1

Comments

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

Links

Table of n, a(n) for n=1..21.

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.

Sequence in context: A220027 A072489 A072487 * A254232 A335831 A189394

Adjacent sequences: A309872 A309873 A309874 * A309876 A309877 A309878

Keyword

nonn

Author

Amiram Eldar, Aug 21 2019

Status

approved