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A128694 Number of groups of order A128693(n). 4
2, 1, 5, 2, 1, 2, 2, 1, 15, 2, 4, 1, 1, 2, 2, 2, 4, 1, 2, 5, 1, 2, 1, 55, 5, 1, 2, 13, 2, 2, 1, 2, 2, 1, 2, 1, 4, 2, 5, 1, 2, 1, 2, 5, 1, 14, 2, 2, 4, 1, 16, 1, 2, 2, 1, 2, 5, 2, 2, 261, 2, 1, 15, 1, 2, 1, 2, 4, 49, 1, 2, 1, 2, 4, 5, 2, 2, 5, 2, 1, 2, 1, 4, 1, 2, 2, 1, 1, 5, 1, 2, 1, 2, 2, 13, 1, 2, 4, 1, 15, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Number of groups for orders of form 3^k*p, where 1 <= k <= 6 and p is a prime different from 3.
The groups of these orders (up to A128693(84005521) = 3221225379 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA.
LINKS
MAGMA Documentation, Database of Small Groups
FORMULA
a(n) = A000001(A128693(n)).
EXAMPLE
A128693(9) = 54 and there are 15 groups of order 54 (A000001(54) = 15), hence a(9) = 15.
PROG
(Magma) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n): n in [ h: h in [1..910] | #t eq 2 and ((t[1, 1] eq 2 and t[1, 2] eq 1 and t[2, 1] eq 3 and t[2, 2] le 6) or (t[1, 1] eq 3 and t[1, 2] le 6 and t[2, 2] eq 1)) where t is Factorization(h) ] ];
CROSSREFS
Cf. A000001 (number of groups of order n), A128693 (numbers of form 3^k*p, 1<=k<=6, p!=3 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 and p>2 prime).
Sequence in context: A355914 A117941 A134566 * A088421 A240394 A259447
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Mar 26 2007
STATUS
approved

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