login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A128645 Number of groups of order A128691(n). 5
2, 2, 5, 2, 5, 2, 15, 2, 4, 2, 2, 14, 4, 2, 52, 5, 13, 2, 2, 5, 2, 4, 52, 2, 2, 12, 4, 2, 231, 14, 2, 43, 5, 2, 2, 4, 2, 15, 2, 2, 5, 12, 2, 238, 5, 2, 4, 42, 2, 12, 4, 1543, 2, 2, 2, 51, 5, 2, 2, 197, 2, 14, 4, 5, 12, 2, 2, 4, 54, 2, 2, 4, 5, 14, 2, 2, 42, 2, 4, 1640, 2, 15, 4, 2, 12, 2, 195, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of groups whose order is of form 2^k*p, where 1 <= k <= 8 and p is a prime > 2.

The groups of these orders (up to A128691(112490698) = 2147483636 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

FORMULA

a(n) = A000001(A128691(n)).

EXAMPLE

A128691(7) = 24 and there are 15 groups of order 24 (A000001(24) = 15), hence a(7) = 15.

PROG

(MAGMA) D := SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ h: h in [1..360] | #t eq 2 and t[1, 1] eq 2 and t[1, 2] le 8 and t[2, 2] eq 1 where t is Factorization(h) ] ];

CROSSREFS

Cf. A000001 (number of groups of order n), A128691 (numbers of form 2^k*p, 1<=k<=8, p > 2 prime), A128604 (number of groups whose order divides p^6 for p a prime), A128644 (number of groups whose order has at most 3 prime factors).

Sequence in context: A233468 A076200 A039931 * A007610 A068066 A171889

Adjacent sequences:  A128642 A128643 A128644 * A128646 A128647 A128648

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Mar 21 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 7 11:46 EDT 2020. Contains 336276 sequences. (Running on oeis4.)