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A055981 a(n) = ceiling(n!/d(n!)). 0
1, 1, 2, 3, 8, 24, 84, 420, 2268, 13440, 73920, 604800, 3931200, 33633600, 324324000, 3891888000, 33081048000, 435891456000, 4140968832000, 59281238016000, 840311548876800, 11708340914350080, 134645920515025920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The ceiling function is required only for n = 3 and 5.

Luca and Yound prove that a(n) divides n! for n >= 6. - Michel Marcus, Nov 02 2017

LINKS

Table of n, a(n) for n=1..23.

Florian Luca and Paul Thomas Young, On the number of divisors of n! and of the Fibonacci numbers, Glasnik Matematicki, Vol. 47, No. 2 (2012), 285-293. DOI: 10.3336/gm.47.2.05.

FORMULA

a(n) = ceiling(A000142(n)/A027423(n)).

EXAMPLE

For n=3 n!=6, d(n!)=4, quotient is 3/2, for n=5 n!=120, d(n!)=16, quotient=15/2. All other cases give integers.

PROG

(PARI) a(n) = ceil(n!/numdiv(n!)); \\ Michel Marcus, Nov 02 2017

CROSSREFS

Cf. A000142, A000005, A033950, A027423.

Sequence in context: A089847 A304121 A038561 * A182212 A120260 A202592

Adjacent sequences:  A055978 A055979 A055980 * A055982 A055983 A055984

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 21 2000

STATUS

approved

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Last modified January 22 19:16 EST 2020. Contains 331153 sequences. (Running on oeis4.)