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A070089 P(n) < P(n+1) where P(n) (A006530) is the largest prime factor of n. 9

%I

%S 1,2,4,6,8,9,10,12,16,18,20,21,22,24,25,27,28,30,32,33,36,40,42,45,46,

%T 48,50,52,54,56,57,58,60,64,66,68,70,72,75,77,78,81,82,84,85,88,90,91,

%U 92,93,96,98,100,102,105,106,108,110,112,114,115,117

%N P(n) < P(n+1) where P(n) (A006530) is the largest prime factor of n.

%C Erdős conjectured that this sequence has asymptotic density 1/2.

%C There are 500149 terms in this sequence up to 10^6, 4999951 up to 10^7, 49997566 up to 10^8, and 499992458 up to 10^9. With a binomial model with p = 1/2, these would be +0.3, -0.5, -0.0, and -0.5 standard deviations from their respective means. In other words, Erdős's conjecture seems solid. - _Charles R Greathouse IV_, Oct 27 2015

%D H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 210.

%H T. D. Noe, <a href="/A070089/b070089.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_] := FactorInteger[n][[ -1, 1]]; Select[ Range[125], f[ # ] < f[ # + 1] &]

%o (PARI) gpf(n)=if(n<3,n,my(f=factor(n)[,1]); f[#f])

%o is(n)=gpf(n) < gpf(n+1) \\ _Charles R Greathouse IV_, Oct 27 2015

%Y Cf. A006530, A070087.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 13 2002

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Last modified October 18 09:46 EDT 2018. Contains 316319 sequences. (Running on oeis4.)