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A037289
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Number of commutative rings with n elements.
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5
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1, 2, 2, 9, 2, 4, 2, 34, 9, 4, 2, 18, 2, 4, 4, 162, 2, 18, 2, 18, 4, 4, 2, 68, 9, 4, 36, 18, 2, 8, 2
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OFFSET
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1,2
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COMMENTS
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This sequence is multiplicative. See the reference "The Numbers of Small Rings" below, which proves the result for all rings; restricting to commutative rings only makes the proof easier. - Conjecture by Mitch Harris, Apr 19 2005, proof found by Franklin T. Adams-Watters, Jul 10 2012
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LINKS
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Table of n, a(n) for n=1..31.
C. Noebauer, Home page
Christof Noebauer, The numbers of small rings (PostScript).
C. Noebauer, Thesis on the enumeration of near-rings
Bjorn Poonen, The moduli space of commutative algebras of finite rank, J. Eur. Math. Soc. (JEMS) 10:3 (2008), pp. 817-836. arXiv:0608491
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FORMULA
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a(p^n) = p^(2/27 * n^3 + O(n^(8/3))), see Theorems 11.2 and 11.3 in Poonen 2008. - Charles R Greathouse IV, Jul 10 2012
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CROSSREFS
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Cf. A027623, A037291.
Sequence in context: A199058 A082838 A074961 * A037290 A155936 A167594
Adjacent sequences: A037286 A037287 A037288 * A037290 A037291 A037292
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KEYWORD
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nonn,nice,more,hard,mult
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AUTHOR
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Christian G. Bower, Jun 15 1998.
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EXTENSIONS
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a(16) from Christof Noebauer (christof.noebauer(AT)algebra.uni-linz.ac.at), Sep 29, 2000, who reports that the sequence continues a(32) = ? (> 876), a(33) = 4, 4, 4, 81, 2, 4, 4, 68, 2, 8, 2, 18, 18, 4, 2, 324, 9, 18, 4, 18, 2, 72, 4, 68, 4, 4, 2, 36, 2, 4, 18 = a(63), a(64) = ? (> 12696)
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STATUS
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approved
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