cp's OEIS Frontend

A128704 Number of groups of order A128703(n).

%I A128704 #15 Mar 15 2025 10:45:23
%S A128704 2,1,1,5,2,1,3,1,1,1,1,2,2,1,2,1,1,15,1,4,1,2,2,1,2,1,7,1,1,2,1,2,1,2,
%T A128704 1,1,1,1,2,1,2,1,1,2,1,2,4,1,1,1,1,5,1,2,2,2,1,1,1,4,2,2,1,1,1,1,2,1,
%U A128704 2,55,2,1,1,2,1,2,15,1,2,1,1,2,4,1,2,1,1,5,2,2,1,1,1,1,4,1,2,1,1,21,1,1,1,2
%N A128704 Number of groups of order A128703(n).
%C A128704 Number of groups for orders of form 5^k*p, where 1 <= k <= 5 and p is a prime different from 5.
%C A128704 The groups of these orders (up to A128703(69556991) = 5368708945 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA.
%H A128704 Klaus Brockhaus, <a href="/A128704/b128704.txt">Table of n, a(n) for n=1..10000</a>
%H A128704 Magma Computational Algebra System, <a href="https://magma.maths.usyd.edu.au/magma/handbook/">Documentation</a>, see Database of Small Groups.
%F A128704 a(n) = A000001(A128703(n)).
%e A128704 A128703(20) = 275 and there are 4 groups of order 275 (A000001(275) = 4), hence a(20) = 4.
%o A128704 (Magma) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n): n in [ h: h in [1..2000] | #t eq 2 and ((t[1, 1] lt 5 and t[1, 2] eq 1 and t[2, 1] eq 5 and t[2, 2] le 5) or (t[1, 1] eq 5 and t[1, 2] le 5 and t[2, 2] eq 1)) where t is Factorization(h) ] ];
%Y A128704 Cf. A000001 (number of groups of order n), A128703 (numbers of form 5^k*p, 1<=k<=5, p!=5 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).
%K A128704 nonn
%O A128704 1,1
%A A128704 _Klaus Brockhaus_, Mar 26 2007