

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
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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 V2.134) form a class contained in the Small Groups Library of MAGMA.


LINKS



FORMULA



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).


KEYWORD

nonn


AUTHOR



STATUS

approved



