A098885 Number of nonisomorphic p^m-groups (i.e., groups of prime power orders).

1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 14, 1, 1, 1, 2, 5, 1, 1, 51, 1, 1, 1, 1, 2, 1, 1, 1, 267, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 1, 2328, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 67, 1, 56092, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Lekraj Beedassy, Oct 14 2004

Keywords

• nonn

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..340 [a(199) corrected by Andrey Zabolotskiy]
• H. U. Besche, B. Eick and E. A. O'Brien, Number of isomorphism types of finite groups of given order [dead link]

Crossrefs

Cf. A000001, A000961, A098886, A128604.

Programs

Magma

D := SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [1..410] | n eq 1 or IsPrimePower(n) ]; /* Klaus Brockhaus, Mar 15 2007 */

Formula

a(n) = A000001(A000961(n)).

Extensions

More terms from Klaus Brockhaus, Mar 15 2007