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A018216
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Maximal number of subgroups in a group with n elements.
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3
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1, 2, 2, 5, 2, 6, 2, 16, 6, 8, 2, 16, 2, 10, 4, 67, 2, 28, 2, 22, 10, 14, 2, 54, 8, 16, 28, 28, 2, 28, 2, 374, 4, 20, 4, 78, 2, 22, 16, 76, 2, 36, 2, 40, 12, 26, 2, 236, 10, 64, 4, 46, 2, 212, 14, 98, 22, 32, 2, 80, 2, 34, 36, 2825, 4, 52, 2, 58, 4, 52, 2, 272
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OFFSET
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1,2
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COMMENTS
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For n >= 2 a(n)>=2 with equality iff n is prime.
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LINKS
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Eric M. Schmidt, Table of n, a(n) for n = 1..511
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FORMULA
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a(n)=Maximum of {A061034(n), A083573(n)}. - Lekraj Beedassy, Oct 22 2004
(C_2)^m has A006116(m) subgroups, so this is a lower bound if n is a power of 2 (e.g. a(16) >= 67). - N. J. A. Sloane, Dec 01 2007
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EXAMPLE
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a(6) = 6 because there are two groups with 6 elements: C_6 with 4 subgroups and S_3 with 6 subgroups.
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CROSSREFS
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Cf. A061034.
Sequence in context: A093663 A011143 A185291 * A059907 A024931 A029648
Adjacent sequences: A018213 A018214 A018215 * A018217 A018218 A018219
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KEYWORD
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nonn,nice
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AUTHOR
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Ola Veshta (olaveshta(AT)my-deja.com), May 23 2001
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EXTENSIONS
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More terms from Victoria A. Sapko (vsapko(AT)canes.gsw.edu), Jun 13 2003
More terms from Eric M. Schmidt, Sep 07 2012
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STATUS
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approved
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