

A001013


JordanPolya numbers: products of factorial numbers A000142.
(Formerly M0993 N0372)


22



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
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OFFSET

1,2


COMMENTS

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^26x+(6x3)a(n)+2a(n)^2+1) = N^2 has an integer solution.  Ralf Stephan, Dec 04 2004


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B23.
Melter, Robert A.; Autometrized unary algebras. J. Combinatorial Theory 5 1968 2129.
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).


LINKS

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


EXAMPLE

864=(3!)^2*4!


MATHEMATICA

For[p=0; a=f=Table[n!, {n, 1, 8}], p=!=a, p=a; a=Select[Union@@Outer[Times, f, a], #<=8!&]]; a


CROSSREFS

Cf. A034878.
Sequence in context: A096850 A062847 * A115746 A025610 A131117 A181821
Adjacent sequences: A001010 A001011 A001012 * A001014 A001015 A001016


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms, formula from Christian G. Bower, Dec 15 1999.
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 17 2002


STATUS

approved



