1,3

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)

Klaus Brockhaus, Table of n, a(n) for n=1..10000

MAGMA Documentation, Database of Small Groups

a(n) = A000001(A128603(n)).

A128603(10) = 16 and there are 14 groups of order 16 (A000001(16) = 14), hence a(10) = 14.

(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)) } ] ];

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: A022661 A120292 A162470 this_sequence A098885 A106270 A047888

Adjacent sequences: A128601 A128602 A128603 this_sequence A128605 A128606 A128607

nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 13 2007