OFFSET
0,3
LINKS
Paul Erdős and Ron L. Graham, On products of factorials, Bull. Inst. Math. Acad. Sinica 4:2 (1976), pp. 337-355.
FORMULA
Erdős and Graham prove that log a(n) ~ n log log n/log n.
a(p) = 2*a(p-1) for prime p. - Jon E. Schoenfield, Apr 01 2015
EXAMPLE
a(3) = |{1!, 2!, 3!, 2!*3!}| = |{1, 2, 6, 12}| = 4.
MAPLE
s:= proc(n) option remember; (f-> `if`(n=0, {f},
map(x-> [x, x*f][], s(n-1))))(n!)
end:
a:= n-> nops(s(n)):
seq(a(n), n=0..20); # Alois P. Heinz, Mar 16 2015
MATHEMATICA
a[n_] := a[n] = If[n == 0, 1, If[PrimeQ[n], 2 a[n-1], Times @@@ ((Subsets[Range[n]] // Rest) /. k_Integer -> k!) // Union // Length]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 23}] (* Jean-François Alcover, May 01 2022 *)
PROG
(PARI) a(n)=my(v=[1], N=n!); for(k=2, n-1, v=Set(concat(v, v*k!))); #v + sum(i=1, #v, !setsearch(v, N*v[i]))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Charles R Greathouse IV, Mar 11 2015
EXTENSIONS
More terms from Alois P. Heinz, Mar 16 2015
a(31) (=2*a(30)) from Jon E. Schoenfield, Apr 01 2015
STATUS
approved