A128645 Number of groups of order A128691(n).

2, 2, 5, 2, 5, 2, 15, 2, 4, 2, 2, 14, 4, 2, 52, 5, 13, 2, 2, 5, 2, 4, 52, 2, 2, 12, 4, 2, 231, 14, 2, 43, 5, 2, 2, 4, 2, 15, 2, 2, 5, 12, 2, 238, 5, 2, 4, 42, 2, 12, 4, 1543, 2, 2, 2, 51, 5, 2, 2, 197, 2, 14, 4, 5, 12, 2, 2, 4, 54, 2, 2, 4, 5, 14, 2, 2, 42, 2, 4, 1640, 2, 15, 4, 2, 12, 2, 195, 5, 2

Offset: 1

Author

Klaus Brockhaus, Mar 21 2007

Keywords

• nonn

Comments

Number of groups whose order is of form 2^k*p, where 1 <= k <= 8 and p is a prime > 2.

The groups of these orders (up to A128691(112490698) = 2147483636 in version V2.13-4) form a class contained in the Small Groups Library of Magma.

Examples

			A128691(7) = 24 and there are 15 groups of order 24 (A000001(24) = 15), hence a(7) = 15.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..10000
• Magma Computational Algebra System, Documentation, see Database of Small Groups.

Crossrefs

Cf. A000001 (number of groups of order n), A128691 (numbers of form 2^k*p, 1<=k<=8, p > 2 prime), A128604 (number of groups whose order divides p^6 for p a prime), A128644 (number of groups whose order has at most 3 prime factors).

Programs

Magma

D := SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ h: h in [1..360] | #t eq 2 and t[1, 1] eq 2 and t[1, 2] le 8 and t[2, 2] eq 1 where t is Factorization(h) ] ];

Formula

a(n) = A000001(A128691(n)).