|
| |
|
|
A128604
|
|
Number of groups of order A128603(n).
|
|
9
| |
|
|
1, 1, 2, 1, 1, 5, 2, 1, 1, 14, 1, 1, 1, 2, 5, 1, 1, 51, 1, 1, 1, 1, 2, 1, 1, 1, 267, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 67, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Number of groups whose order divides p^6 for p a prime.
The groups of these orders (up to A128603(54403784) = 1073741789 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA. (corrected Mar 18 2007)
|
|
|
LINKS
| Klaus Brockhaus, Table of n, a(n) for n=1..10000
MAGMA Documentation, Database of Small Groups
|
|
|
FORMULA
| a(n) = A000001(A128603(n)).
|
|
|
EXAMPLE
| A128603(10) = 16 and there are 14 groups of order 16 (A000001(16) = 14), hence a(10) = 14.
|
|
|
PROG
| (MAGMA) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ k: k in [1..455] | exists(t) {x: x in [t: t in [1..6] ] | IsPower(k, x) and IsPrime(Iroot(k, x)) } ] ];
|
|
|
CROSSREFS
| Cf. A000001 (number of groups of order n), A128603 (numbers dividing p^6 for p a prime), A098885 (number of groups of prime power orders).
Sequence in context: A179318 A162470 A174004 * A098885 A106270 A047888
Adjacent sequences: A128601 A128602 A128603 * A128605 A128606 A128607
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 13 2007
|
| |
|
|
