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A128604
Number of groups of order A128603(n).
11
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)
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
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Mar 13 2007
STATUS
approved