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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

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OFFSET

1,4

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]

FORMULA

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

PROG

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

CROSSREFS

Cf. A000001, A000961, A098886, A128604.