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