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

1,2

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.

Links

Table of n, a(n) for n=1..13.

Example

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.

Sequence in context: A306892 A387062 A115275 * A000679 A266932 A243787

Adjacent sequences: A384603 A384604 A384605 * A384607 A384608 A384609

Keyword

nonn,more,hard

Author

Robin Jones, Jun 04 2025

Status

approved