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A058295
Products of distinct factorials.
19
1, 2, 6, 12, 24, 48, 120, 144, 240, 288, 720, 1440, 2880, 4320, 5040, 5760, 8640, 10080, 17280, 30240, 34560, 40320, 60480, 80640, 86400, 103680, 120960, 172800, 207360, 241920, 362880, 483840, 518400, 604800, 725760, 967680, 1036800, 1209600
OFFSET
1,2
COMMENTS
(A075082(n)!)^2 is a member for n>0, for example, (6!)^2=6!*5!*3!. Factorials A000142 and superfactorials A000178 (without their first terms), double-superfactorials A098694 and product-of-next-n-factorials A074319 are all subsequences. Products-of-factorials A001013 is a supersequence. - Jonathan Sondow, Dec 18 2004
A000197(n)^2 is a member for n > 2, as ((n!)!)^2 = (n!)!*n!*(n!-1)!. - Jonathan Sondow, Dec 21 2004
Erdős & Graham show that there are exp((1+o(1))n log log n / log n) members of this sequence using no factorials above n.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Paul Erdős and Ron L. Graham, On products of factorials, Bull. Inst. Math. Acad. Sinica 4:2 (1976), pp. 337-355.
EXAMPLE
288 is included because 288 = 2! * 3! * 4!.
MATHEMATICA
k=10; m=1; With[{p=With[{s=Subsets[Table[n!, {n, 2, k}]]}, Sort[Table[Apply[Times, s[[n]]], {n, Length[s]}]]]}, While[p[[m]]<(k+1)!, m++ ]; Union[Take[p, m-1]]] (* Jonathan Sondow *)
PROG
(PARI) list(lim)=my(v=List([1]), n=1, t=1); while((t=n++!)<=lim, for(i=1, #v, if(v[i]*t<=lim, listput(v, v[i]*t)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Mar 26 2012
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 07 2000
EXTENSIONS
Corrected by Jonathan Sondow, Dec 18 2004
STATUS
approved