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 A058295 Products of distinct factorials. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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(), 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 CROSSREFS Cf. A075082, A000142, A000178, A098694, A074319, A001013, A000197. Sequence in context: A003680 A051487 A111286 * A309841 A132176 A197469 Adjacent sequences:  A058292 A058293 A058294 * A058296 A058297 A058298 KEYWORD nonn AUTHOR Leroy Quet, Dec 07 2000 EXTENSIONS Corrected by Jonathan Sondow, Dec 18 2004 STATUS approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)