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 A057109 Numbers n that are not factors of P(n)!, where P(n) is the largest prime factor of n. 11
 4, 8, 9, 12, 16, 18, 24, 25, 27, 32, 36, 45, 48, 49, 50, 54, 64, 72, 75, 80, 81, 90, 96, 98, 100, 108, 121, 125, 128, 135, 144, 147, 150, 160, 162, 169, 175, 180, 189, 192, 196, 200, 216, 224, 225, 240, 242, 243, 245, 250, 256, 270, 288, 289, 294, 300, 320, 324 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These are also the numbers for which the Kempner function A002034 is composite. Their density approaches zero as they go to infinity. - Jud McCranie, Dec 08 2001 n is a member if and only if P(n) < A002034(n). The members are the exceptions to the rule that P(n) = A002034(n) for almost all n (Erdős and Kastanas 1994, Ivic 2004). - Jonathan Sondow, Jan 10 2005 Same as numbers n such that |e - m/n| < 1/(P(n)+1)! for some integer m. - Jonathan Sondow, Dec 29 2007 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 284-292. LINKS Paul Erdős and Ilias Kastanas, Solution 6674: The smallest factorial that is a multiple of n, Amer. Math. Monthly 101 (1994) 179. S. R. Finch, The Average Value of the Smarandache Function A. Ivic (2004), On a problem of Erdos involving the largest prime factor of n, arXiv:math/0311056 [math.NT], 2003-2004. C. Rivera, Conjecture about their density 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 EXAMPLE 12 is in the sequence since 3 is the largest prime factor of 12, but 12 is not a factor of 3! = 6. MAPLE with(numtheory): for n from 2 to 800 do if ifactors(n)[2][nops(ifactors(n)[2])][1]! mod n <> 0 then printf(`%d, `, n) fi; od: MATHEMATICA Select[Range[330], Mod[FactorInteger[#][[-1, 1]]!, #] != 0 &] (* Jean-François Alcover, May 19 2011 *) PROG (PARI) is(n)=my(s=factor(n)[, 1]); s[#s]!%n>0 \\ Charles R Greathouse IV, Sep 20 2012 CROSSREFS Subsequence of A122145. Cf. A002034, A006530, A057108. Sequence in context: A048098 A122145 A034030 * A069189 A283050 A069168 Adjacent sequences:  A057106 A057107 A057108 * A057110 A057111 A057112 KEYWORD easy,nonn AUTHOR Henry Bottomley, Aug 08 2000 EXTENSIONS More terms from James A. Sellers, Aug 22 2000 STATUS approved

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