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 A055981 a(n) = ceiling(n!/d(n!)). 1
 1, 1, 2, 3, 8, 24, 84, 420, 2268, 13440, 73920, 604800, 3931200, 33633600, 324324000, 3891888000, 33081048000, 435891456000, 4140968832000, 59281238016000, 840311548876800, 11708340914350080, 134645920515025920, 2554547108585472000, 45616912653312000000 (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 Amiram Eldar, Table of n, a(n) for n = 1..471 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)). Sum_{n>=1} 1/a(n) = A071815 - 7/40. - Amiram Eldar, Apr 23 2021 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. MATHEMATICA a[n_] := Ceiling[n!/DivisorSigma[0, n!]]; Array[a, 30] (* Amiram Eldar, Apr 23 2021 *) PROG (PARI) a(n) = ceil(n!/numdiv(n!)); \\ Michel Marcus, Nov 02 2017 CROSSREFS Cf. A000142, A000005, A033950, A027423, A071815. 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 EXTENSIONS More terms from Amiram Eldar, Apr 23 2021 STATUS approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)