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A128706 Number of groups of order A128705(n). 2
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; refs; listen; history; text; internal format)
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

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.

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).

Sequence in context: A242618 A180264 A225200 * A253586 A318191 A208183

Adjacent sequences:  A128703 A128704 A128705 * A128707 A128708 A128709

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Mar 26 2007

STATUS

approved

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Last modified September 15 18:22 EDT 2019. Contains 327082 sequences. (Running on oeis4.)