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

1,1

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.

Links

Klaus Brockhaus, Table of n, a(n) for n = 1..10000

Magma Documentation, Database of Small Groups

Formula

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

Example

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

Prog

(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) ] ];

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).

Sequence in context: A233468 A076200 A039931 * A007610 A068066 A171889

Adjacent sequences: A128642 A128643 A128644 * A128646 A128647 A128648

Keyword

nonn

Author

Klaus Brockhaus, Mar 21 2007

Status

approved