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A101976 Number of products of factorials not exceeding n!. 2
1, 2, 4, 8, 15, 28, 49, 83, 134, 209, 317, 473, 687, 987, 1403, 1972, 2732, 3752, 5096, 6852, 9144, 12113, 15919, 20802, 27012, 34860, 44755, 57136, 72592, 91802, 115567, 144916, 180963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the position of n! in A001013 (Jordan-Polya numbers: products of factorials). a(n) > A101977(n) for n > 2 and a(n) > A101978(n) for n > 3.

LINKS

Table of n, a(n) for n=1..33.

Index entries for sequences related to factorial numbers.

Eric Weisstein's World of Mathematics, Factorial Products

EXAMPLE

a(4) = 8 because 8 products of factorials do not exceed 4!, namely, 1, 2, 4, 6, 8, 12, 16 and 24.

MATHEMATICA

m[n_]:=(For[p=0; a=f=Table[k!, {k, 1, n}], p=!=a, p=a; a=Select[Union@@Outer[Times, f, a], #<=n!&]]; a); Table[Length[m[n]], {n, 20}]

CROSSREFS

Cf. A000142, A001013, A101977, A101978.

Sequence in context: A222028 A338760 A056181 * A339656 A196723 A036615

Adjacent sequences:  A101973 A101974 A101975 * A101977 A101978 A101979

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Dec 22 2004

EXTENSIONS

a(21)-a(33) from Donovan Johnson, May 30 2012

STATUS

approved

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Last modified April 12 18:58 EDT 2021. Contains 342932 sequences. (Running on oeis4.)