A128604 Number of groups of order A128603(n).

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

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

Index entries for sequences related to 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: A162470 A343234 A174004 * A098885 A106270 A319171

Adjacent sequences: A128601 A128602 A128603 * A128605 A128606 A128607

Keyword

nonn

Author

Klaus Brockhaus, Mar 13 2007

Status

approved