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Search: id:A128704
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| 2, 1, 1, 5, 2, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 15, 1, 4, 1, 2, 2, 1, 2, 1, 7, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 1, 1, 5, 1, 2, 2, 2, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 2, 1, 2, 55, 2, 1, 1, 2, 1, 2, 15, 1, 2, 1, 1, 2, 4, 1, 2, 1, 1, 5, 2, 2, 1, 1, 1, 1, 4, 1, 2, 1, 1, 21, 1, 1, 1, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Number of groups for orders of form 5^k*p, where 1 <= k <= 5 and p is a prime different from 5.
The groups of these orders (up to A128703(69556991) = 5368708945 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA.
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..10000
MAGMA Documentation, Database of Small Groups
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FORMULA
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a(n) = A000001(A128703(n)).
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EXAMPLE
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A128703(20) = 275 and there are 4 groups of order 275 (A000001(275) = 4), hence a(20) = 4.
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PROGRAM
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(MAGMA) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n): n in [ h: h in [1..2000] | #t eq 2 and ((t[1, 1] lt 5 and t[1, 2] eq 1 and t[2, 1] eq 5 and t[2, 2] le 5) or (t[1, 1] eq 5 and t[1, 2] le 5 and t[2, 2] eq 1)) where t is Factorization(h) ] ];
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CROSSREFS
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Cf. A000001 (number of groups of order n), A128703 (numbers of form 5^k*p, 1<=k<=5, p!=5 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, p>2 prime), A128694 (number of groups for orders of form 3^k*p, 1<=k<=6, p!=3 prime.
Sequence in context: A098885 A106270 A047888 this_sequence A075259 A003570 A011281
Adjacent sequences: A128701 A128702 A128703 this_sequence A128705 A128706 A128707
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 26 2007
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