cp's OEIS Frontend

A128706 Number of groups of order A128705(n).

%I A128706 #15 Mar 15 2025 10:45:29
%S A128706 2,2,1,1,1,5,1,1,6,1,2,1,2,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,15,1,1,1,1,
%T A128706 2,2,2,1,2,1,1,19,1,1,1,2,1,1,1,1,1,1,1,2,1,4,2,2,1,1,1,1,2,1,5,1,1,2,
%U A128706 1,1,1,1,2,1,2,1,4,1,1,1,1,2,1,2,1,1,1,1,1,2,1,2,1,1,1,1,1,2,1,2,2,1,1,1,1
%N A128706 Number of groups of order A128705(n).
%C A128706 Number of groups for orders of form 7^k*p, where 1 <= k <= 4 and p is a prime different from 7.
%C A128706 The groups of these orders (up to A128705(64633879) = 7516192523 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA.
%H A128706 Klaus Brockhaus, <a href="/A128706/b128706.txt">Table of n, a(n) for n=1..10000</a>
%H A128706 Magma Computational Algebra System, <a href="https://magma.maths.usyd.edu.au/magma/handbook/">Documentation</a>, see Database of Small Groups.
%F A128706 a(n) = A000001(A128705(n)).
%e A128706 A128705(30) = 686 and there are 15 groups of order 686 (A000001(686) = 15), hence a(30) = 15.
%o A128706 (Magma) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n): n in [ h: h in [1..3500] | #t eq 2 and ((t[1, 1] lt 7 and t[1, 2] eq 1 and t[2, 1] eq 7 and t[2, 2] le 4) or (t[1, 1] eq 7 and t[1, 2] le 4 and t[2, 2] eq 1)) where t is Factorization(h) ] ];
%Y A128706 Cf. A000001 (number of groups of order n), A128705 (numbers of form 7^k*p, 1<=k<=4, p!=7 prime), A128604 (number of groups for orders that divide p^6, p prime), A128644 (number of groups for orders that have at most 3 prime factors), A128645 (number of groups for orders of form 2^k*p, 1<=k<=8, p>2 prime), A128694 (number of groups for orders of form 3^k*p, 1<=k<=6, p!=3 prime), A128704 (number of groups for orders of form 5^k*p, 1<=k<=5, p!=5 prime).
%K A128706 nonn
%O A128706 1,1
%A A128706 _Klaus Brockhaus_, Mar 26 2007