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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 (list; graph; refs; listen; history; text; internal format)
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) 637-641.

J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010.

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]] (* Jean-Fran├žois 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

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Last modified May 12 15:33 EDT 2021. Contains 343825 sequences. (Running on oeis4.)