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A255937 Number of distinct products of distinct factorials up to n!. 1
1, 1, 2, 4, 8, 16, 28, 56, 108, 204, 332, 664, 1114, 2228, 4078, 7018, 11402, 22804, 40638, 81276, 140490, 230328, 391544, 783088, 1287034, 2273676, 3903626, 6837760, 10368184, 20736368, 34081198, 68162396 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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

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

Cf. A058295, A000142, A001013, A060957.

Sequence in context: A208531 A054189 A127195 * A177269 A018726 A049884

Adjacent sequences:  A255934 A255935 A255936 * A255938 A255939 A255940

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

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)