cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A098886 #15 Jun 07 2022 02:29:55
%S A098886 1,2,5,2,14,2,5,51,2,267,15,2,5,2328,2,67,56092,2,5,2,10494213,2,15,
%T A098886 504,2,2,49487367289,5,2,2,2
%N A098886 Number of nonisomorphic groups with prime power order p^m, m>1.
%H A098886 H. U. Besche, B. Eick and E. A. O'Brien, <a href="http://www.icm.tu-bs.de/ag_algebra/software/small/number.html">Number of isomorphism types of finite groups of given order</a>
%H A098886 David Burrell, <a href="https://doi.org/10.1080/00927872.2021.2006680">On the number of groups of order 1024</a>, Communications in Algebra, 2021, 1-3.
%F A098886 a(n) = A000001(A025475(n)).
%o A098886 (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 */
%Y A098886 Cf. A000001, A025475, A098885, A128604.
%K A098886 nonn
%O A098886 1,2
%A A098886 _Lekraj Beedassy_, Oct 14 2004
%E A098886 a(30) corrected by _Klaus Brockhaus_, Mar 15 2007
%E A098886 a(27) corrected by _David Burrell_, Jun 06 2022