A384607 -id:A384607 - cp's OEIS frontend

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

Robin Jones, Jun 04 2025

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.

			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.

Cf. A098885, A384607.

A384609 Possible values for the number of nilpotent groups of a finite order, ordered by size.

Original entry on oeis.org

1, 2, 4, 5, 8, 10, 14, 15, 16, 20, 25, 28, 30, 32, 40, 50, 51, 56, 60, 64, 67, 70, 75, 77, 80, 83, 87, 97, 100, 101, 102, 107, 111, 112, 120, 125, 128, 131, 134, 140, 145, 149, 150, 154, 155, 159, 160, 166, 173, 174, 183, 193, 194, 196, 200, 202, 203, 204, 207

Offset: 1

Robin Jones, Jun 04 2025

nonn

A066060 sorted and duplicates removed.

List of all possible products of terms in A384607 (possibly with use of the same integer more than once).

			1 is in this sequence as there is exactly 1 nilpotent group of order 1.
2 is in this sequence as there are exactly 2 nilpotent groups of order 4.
4 is in this sequence as there are exactly 4 nilpotent groups of order 36.
3 is not in this sequence as there are never exactly 3 nilpotent groups of any given order.

Robin Jones, Table of n, a(n) for n = 1..135

Cf. A066060, A384607.

cp's OEIS Frontend

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

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