

A122380


Numbers n such that n^2 > P(n)!, where P(n) is the greatest prime factor of n.


2



2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 147, 150, 160, 162, 168, 175, 180, 189, 192, 196, 200, 210, 216, 224, 225, 240, 243, 245
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OFFSET

1,1


COMMENTS

It is conjectured that n^2 < P(n)! for almost all n.


LINKS

Table of n, a(n) for n=1..61.
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.
J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function
Index entries for sequences related to factorial numbers.


EXAMPLE

15^2 = 225 > 120 = 5! = P(15)!, so 15 is a member.


MATHEMATICA

Reap[For[n = 2, n <= 250, n++, If[n^2 > FactorInteger[n][[1, 1]]!, Print[n]; Sow[n]]]][[2, 1]] (* JeanFrançois Alcover, Feb 04 2019 *)


CROSSREFS

Cf. A000290, A006530, A057109, A102068, A122378, A122379.
Sequence in context: A036407 A145807 A278962 * A033501 A336504 A331827
Adjacent sequences: A122377 A122378 A122379 * A122381 A122382 A122383


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Sep 03 2006


STATUS

approved



