

A001013


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


25



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.
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 and R. Zumkeller, Table of n, a(n) for n = 1..10000, first 987 terms by T. D. Noe
Robert A. Melter, Autometrized unary algebras, J. Combinatorial Theory 5 1968 2129.
Eric Weisstein's World of Mathematics, Factorial Products
Index entries for sequences related to factorial numbers
Index entries for sequences related to trees


EXAMPLE

864 = (3!)^2*4!.


MAPLE

N:= 10000: # get all terms <= N
S:= {1}:
for k from 2 do
kf:= k!;
if kf > N then break fi;
S := S union {seq(seq(kf^j * s, j = 1 .. floor(log[kf](N/s))), s=S)};
od:
S; # if using Maple 11 or earlier, uncomment the next line:
# sort(convert(S, list));
# Robert Israel, Sep 09 2014


MATHEMATICA

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


PROG

(Sage)
# For the function 'prod_hull' see A246663.
prod_hull(factorial, 5760) # Peter Luschny, Sep 09 2014
(Haskell)
import Data.Set (empty, fromList, deleteFindMin, union)
import qualified Data.Set as Set (null)
a001013 n = a001013_list !! (n1)
a001013_list = 1 : h 0 empty [1] (drop 2 a000142_list) where
h z s mcs xs'@(x:xs)
 Set.null s  x < m = h z (union s (fromList $ map (* x) mcs)) mcs xs
 m == z = h m s' mcs xs'
 otherwise = m : h m (union s' (fromList (map (* m) $ init (m:mcs)))) (m:mcs) xs'
where (m, s') = deleteFindMin s
 Reinhard Zumkeller, Nov 13 2014


CROSSREFS

Cf. A034878.
Sequence in context: A096850 A062847 * A115746 A025610 A242101 A131117
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, Sep 17 2002


STATUS

approved



