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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 Klaus Brockhaus, Table of n, a(n) for n=1..10000 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: A108790 A117941 A134566 * A088421 A240394 A259447 Adjacent sequences:  A128691 A128692 A128693 * A128695 A128696 A128697 KEYWORD nonn AUTHOR Klaus Brockhaus, Mar 26 2007 STATUS approved

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Last modified February 27 15:16 EST 2020. Contains 332307 sequences. (Running on oeis4.)