A128694 Number of groups of order A128693(n).

2, 1, 5, 2, 1, 2, 2, 1, 15, 2, 4, 1, 1, 2, 2, 2, 4, 1, 2, 5, 1, 2, 1, 55, 5, 1, 2, 13, 2, 2, 1, 2, 2, 1, 2, 1, 4, 2, 5, 1, 2, 1, 2, 5, 1, 14, 2, 2, 4, 1, 16, 1, 2, 2, 1, 2, 5, 2, 2, 261, 2, 1, 15, 1, 2, 1, 2, 4, 49, 1, 2, 1, 2, 4, 5, 2, 2, 5, 2, 1, 2, 1, 4, 1, 2, 2, 1, 1, 5, 1, 2, 1, 2, 2, 13, 1, 2, 4, 1, 15, 2

Offset

1,1

Comments

Number of groups for orders of form 3^k*p, where 1 <= k <= 6 and p is a prime different from 3.

The groups of these orders (up to A128693(84005521) = 3221225379 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(A128693(n)).

Example

A128693(9) = 54 and there are 15 groups of order 54 (A000001(54) = 15), hence a(9) = 15.

Prog

(Magma) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n): n in [ h: h in [1..910] | #t eq 2 and ((t[1, 1] eq 2 and t[1, 2] eq 1 and t[2, 1] eq 3 and t[2, 2] le 6) or (t[1, 1] eq 3 and t[1, 2] le 6 and t[2, 2] eq 1)) where t is Factorization(h) ] ];

Crossrefs

Cf. A000001 (number of groups of order n), A128693 (numbers of form 3^k*p, 1<=k<=6, p!=3 prime), A128604 (number of groups for orders that divide p^6, p prime), A128644 (number of groups for orders that have at most 3 prime factors), A128645 (number of groups for orders of form 2^k*p, 1<=k<=8 and p>2 prime).

Sequence in context: A355914 A117941 A134566 * A088421 A240394 A259447

Adjacent sequences: A128691 A128692 A128693 * A128695 A128696 A128697

Keyword

nonn

Author

Klaus Brockhaus, Mar 26 2007

Status

approved