A384606 Possible values for the number of groups of order equal to a prime power, in order of first appearance.

1, 2, 5, 14, 51, 267, 15, 2328, 67, 56092, 10494213, 504, 49487367289

Offset: 1

Author

Robin Jones, Jun 04 2025

Keywords

• nonn
• more
• hard

Comments

Equal A098885 with the duplicate entries removed.

a(14) = A000001(2048) (this value is currently unknown).

This sequence is the same regardless of whether 1 is considered a prime power or not (see A000961 for discussion on this) as A000001(1) = A000001(p) = 1 for all p.

Examples

			1 is in this sequence because A000001(2) = 1.
2 is in this sequence because A000001(2^2) = 2.
5 is in this sequence because A000001(2^3) = 5.
3 is not in this sequence as no prime power p^k has A000001(p^k)=3.
		

Crossrefs

Cf. A098885, A384607.