|
Search: id: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, 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, 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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
|
K. Brockhaus, Table of n, a(n) for n=1..10000
MAGMA Documentation, Database of Small Groups
|
|
FORMULA
|
a(n) = A000001(A128705(n)).
|
|
EXAMPLE
|
A128705(30) = 686 and there are 15 groups of order 686 (A000001(686) = 15), hence a(30) = 15.
|
|
PROGRAM
|
(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).
Sequence in context: A134513 A140751 A104320 this_sequence A090737 A072550 A037810
Adjacent sequences: A128703 A128704 A128705 this_sequence A128707 A128708 A128709
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 26 2007
|
|
|
Search completed in 0.002 seconds
|
