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

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

Author

Robin Jones, Jun 04 2025

Keywords

• nonn

Comments

A066060 sorted and duplicates removed.

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A066060, A384607.