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Search: id:A001013
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| A001013 |
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Jordan-Polya numbers: products of factorial numbers A000142.
(Formerly M0993 N0372)
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+0
21
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| 1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 120, 128, 144, 192, 216, 240, 256, 288, 384, 432, 480, 512, 576, 720, 768, 864, 960, 1024, 1152, 1296, 1440, 1536, 1728, 1920, 2048, 2304, 2592, 2880, 3072, 3456, 3840, 4096, 4320, 4608, 5040, 5184, 5760
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Possible orders of automorphism groups of trees.
Except for the numbers 2, 9 and 10 this sequence is conjectured to be the same as A034878.
Equivalently, a(n)/6*(6x^2-6x+(6x-3)a(n)+2a(n)^2+1) = N^2 has an integer solution. - Ralf Stephan, Dec 04 2004
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B23.
Melter, Robert A.; Autometrized unary algebras. J. Combinatorial Theory 5 1968 21-29.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..987
Eric Weisstein's World of Mathematics, Factorial Products
Index entries for sequences related to trees
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EXAMPLE
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864=(3!)^2*4!
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MATHEMATICA
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For[p=0; a=f=Table[n!, {n, 1, 8}], p=!=a, p=a; a=Select[Union@@Outer[Times, f, a], #<=8!&]]; a
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CROSSREFS
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Cf. A034878.
Sequence in context: A070175 A096850 A062847 this_sequence A115746 A025610 A131117
Adjacent sequences: A001010 A001011 A001012 this_sequence A001014 A001015 A001016
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, formula from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 17 2002
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