

A128645


Number of groups of order A128691(n).


5



2, 2, 5, 2, 5, 2, 15, 2, 4, 2, 2, 14, 4, 2, 52, 5, 13, 2, 2, 5, 2, 4, 52, 2, 2, 12, 4, 2, 231, 14, 2, 43, 5, 2, 2, 4, 2, 15, 2, 2, 5, 12, 2, 238, 5, 2, 4, 42, 2, 12, 4, 1543, 2, 2, 2, 51, 5, 2, 2, 197, 2, 14, 4, 5, 12, 2, 2, 4, 54, 2, 2, 4, 5, 14, 2, 2, 42, 2, 4, 1640, 2, 15, 4, 2, 12, 2, 195, 5, 2
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OFFSET

1,1


COMMENTS

Number of groups whose order is of form 2^k*p, where 1 <= k <= 8 and p is a prime > 2.
The groups of these orders (up to A128691(112490698) = 2147483636 in version V2.134) 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(A128691(n)).


EXAMPLE

A128691(7) = 24 and there are 15 groups of order 24 (A000001(24) = 15), hence a(7) = 15.


PROG

(MAGMA) D := SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ h: h in [1..360]  #t eq 2 and t[1, 1] eq 2 and t[1, 2] le 8 and t[2, 2] eq 1 where t is Factorization(h) ] ];


CROSSREFS

Cf. A000001 (number of groups of order n), A128691 (numbers of form 2^k*p, 1<=k<=8, p > 2 prime), A128604 (number of groups whose order divides p^6 for p a prime), A128644 (number of groups whose order has at most 3 prime factors).
Sequence in context: A233468 A076200 A039931 * A007610 A068066 A171889
Adjacent sequences: A128642 A128643 A128644 * A128646 A128647 A128648


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Mar 21 2007


STATUS

approved



