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A122379 Numbers n such that S(n)! > n^2 > P(n)!, where S(n)! is the smallest factorial divisible by n and P(n) is the greatest prime factor of n. 5
4, 9, 16, 18, 25, 27, 32, 50, 54, 64, 75, 81, 96, 98, 100, 108, 125, 128, 135, 147, 150, 160, 162, 175, 189, 192, 196, 200, 216, 225, 243, 245, 250, 256, 270, 294, 300, 324, 343, 350, 375, 378, 392, 400, 405, 432, 441, 450, 486, 490, 500, 512, 525, 540, 567 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It is conjectured that n^2 < P(n)! for almost all n. It is known that S(n) = P(n) for almost all n. Clearly, S(n) >= P(n) for all n > 1.
LINKS
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
EXAMPLE
S(9)! = 6! = 720 > 81 = 9^2 > 6 = 3! = P(9)!, so 9 is a member.
MATHEMATICA
s[n_] := For[k = 1, True, k++, If[Divisible[k!, n], Return[k]]];
p[n_] := FactorInteger[n][[-1, 1]];
okQ[n_] := s[n]! > n^2 > p[n]!;
Select[Range[1000], okQ] (* Jean-François Alcover, Jan 27 2019 *)
CROSSREFS
Sequence in context: A066925 A313321 A313322 * A104020 A066694 A235993
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Sep 03 2006
STATUS
approved

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Last modified March 29 21:18 EDT 2024. Contains 371281 sequences. (Running on oeis4.)