cp's OEIS Frontend

A128645 Number of groups of order A128691(n).

%I A128645 #15 Mar 15 2025 10:45:07
%S A128645 2,2,5,2,5,2,15,2,4,2,2,14,4,2,52,5,13,2,2,5,2,4,52,2,2,12,4,2,231,14,
%T A128645 2,43,5,2,2,4,2,15,2,2,5,12,2,238,5,2,4,42,2,12,4,1543,2,2,2,51,5,2,2,
%U A128645 197,2,14,4,5,12,2,2,4,54,2,2,4,5,14,2,2,42,2,4,1640,2,15,4,2,12,2,195,5,2
%N A128645 Number of groups of order A128691(n).
%C A128645 Number of groups whose order is of form 2^k*p, where 1 <= k <= 8 and p is a prime > 2.
%C A128645 The groups of these orders (up to A128691(112490698) = 2147483636 in version V2.13-4) form a class contained in the Small Groups Library of Magma.
%H A128645 Klaus Brockhaus, <a href="/A128645/b128645.txt">Table of n, a(n) for n = 1..10000</a>
%H A128645 Magma Computational Algebra System, <a href="https://magma.maths.usyd.edu.au/magma/handbook/">Documentation</a>, see Database of Small Groups.
%F A128645 a(n) = A000001(A128691(n)).
%e A128645 A128691(7) = 24 and there are 15 groups of order 24 (A000001(24) = 15), hence a(7) = 15.
%o A128645 (Magma) D := SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ h: h in [1..360] | #t eq 2 and t[1, 1] eq 2 and t[1, 2] le 8 and t[2, 2] eq 1 where t is Factorization(h) ] ];
%Y A128645 Cf. A000001 (number of groups of order n), A128691 (numbers of form 2^k*p, 1<=k<=8, p > 2 prime), A128604 (number of groups whose order divides p^6 for p a prime), A128644 (number of groups whose order has at most 3 prime factors).
%K A128645 nonn
%O A128645 1,1
%A A128645 _Klaus Brockhaus_, Mar 21 2007