1,1

These are also the numbers whose Smarandache function is composite. Their density approaches zero as they go to infinity. - Jud McCranie (j.mccranie(AT)comcast.net), 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 (Erdos and Kastanas 1994, Ivic 2004). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 10 2005

Same as numbers n such that |e - m/n| < 1/(P(n)+1)! for some integer m. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 29 2007

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 284-292.

P. Erdos and I. Kastanas, Problem/Solution 6674:The smallest factorial that is a multiple of n, Amer. Math. Monthly 101 (1994) 179.

J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.

S. R. Finch, The Average Value of the Smarandache Function

C. Rivera, Conjecture about their density

Eric Weisstein's World of Mathematics, Smarandache function

A. Ivic (2004), On a problem of Erdos involving the largest prime factor of n

J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality

12 is in the sequence since 3 is the largest prime factor of 12, but 12 is not a factor of 3!=6.

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:

Cf. A002034, A006530, A057108.

Sequence in context: A053443 A048098 A122145 this_sequence A069189 A069168 A102211

Adjacent sequences: A057106 A057107 A057108 this_sequence A057110 A057111 A057112

easy,nonn

Henry Bottomley (se16(AT)btinternet.com), Aug 08 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000