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

Author

Tom Harris, Mar 08 2024

Keywords

• nonn
• easy

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

• 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.