A098886 Number of nonisomorphic groups with prime power order p^m, m>1.

1, 2, 5, 2, 14, 2, 5, 51, 2, 267, 15, 2, 5, 2328, 2, 67, 56092, 2, 5, 2, 10494213, 2, 15, 504, 2, 2, 49487367289, 5, 2, 2, 2

Offset: 1

Author

Lekraj Beedassy, Oct 14 2004

Keywords

• nonn

Links

• H. U. Besche, B. Eick and E. A. O'Brien, Number of isomorphism types of finite groups of given order
• David Burrell, On the number of groups of order 1024, Communications in Algebra, 2021, 1-3.

Crossrefs

Cf. A000001, A025475, A098885, A128604.

Programs

Magma

/* Program returns -1 for an order o if the groups of that order are not contained in the Small Groups Library */ D := SmallGroupDatabase(); S := []; for o in [1..2047] do if (o eq 1 or IsPrimePower(o)) and not IsPrime(o) then if IsInSmallGroupDatabase(D, o) then a := NumberOfSmallGroups(D, o); else a := -1; end if; Append(~S, a); end if; end for; S; /* Klaus Brockhaus, Mar 15 2007 */

Formula

a(n) = A000001(A025475(n)).

Extensions

a(30) corrected by Klaus Brockhaus, Mar 15 2007

a(27) corrected by David Burrell, Jun 06 2022