A371022 Numbers k with the property that there is a finite set W of groups of order divisible by k such that if k divides the order of a group G, then G has a subgroup isomorphic to a group in W.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 34, 37, 41, 43, 47, 49, 50, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199

Offset

1,1

Comments

These are called Cauchy numbers in Cameron et al., where they are proved to be the following set: 6 U prime powers U numbers of the form 2*p^a where p is a Fermat prime greater than 3.

Links

Table of n, a(n) for n=1..64.

Peter J. Cameron, David Craven, Hamid Reza Dorbidi, Scott Harper, and Benjamin Sambale, Minimal Cover Groups, arXiv:2311.15652 [math.GR], 2023-2024.

Crossrefs

Cf. A000961, A019434.

Sequence in context: A101373 A371421 A344974 * A107062 A178538 A332166

Adjacent sequences: A371019 A371020 A371021 * A371023 A371024 A371025

Keyword

nonn,easy

Author

Tom Harris, Mar 08 2024

Status

approved