OFFSET
1,1
COMMENTS
Number of groups for orders of form 7^k*p, where 1 <= k <= 4 and p is a prime different from 7.
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.
LINKS
Klaus Brockhaus, Table of n, a(n) for n=1..10000
MAGMA Documentation, Database of Small Groups
EXAMPLE
PROG
(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) ] ];
CROSSREFS
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).
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Mar 26 2007
STATUS
approved