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A128645
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Number of groups of order A128691(n).
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 V2.13-4) form a class contained in the Small Groups Library of MAGMA.
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LINKS
| Klaus Brockhaus, Table of n, a(n) for n=1..10000
MAGMA Documentation, Database of Small Groups
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FORMULA
| a(n) = A000001(A128691(n)).
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EXAMPLE
| A128691(7) = 24 and there are 15 groups of order 24 (A000001(24) = 15), hence a(7) = 15.
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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) ] ];
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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: A153078 A076200 A039931 * A007610 A068066 A171889
Adjacent sequences: A128642 A128643 A128644 * A128646 A128647 A128648
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KEYWORD
| nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 21 2007
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