

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
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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

David A. Corneth, Table of n, a(n) for n = 1..10000
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637641.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 20072010.
Index entries for sequences related to factorial numbers.


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] (* JeanFrançois Alcover, Jan 27 2019 *)


CROSSREFS

Cf. A000290, A002034, A006530, A057109, A092495, A102068, A122378, A122380.
Sequence in context: A066925 A313321 A313322 * A104020 A066694 A235993
Adjacent sequences: A122376 A122377 A122378 * A122380 A122381 A122382


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Sep 03 2006


STATUS

approved



