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A070087 P(n) > P(n+1) where P(n) (A006530) is the largest prime factor of n. 11


%S 3,5,7,11,13,14,15,17,19,23,26,29,31,34,35,37,38,39,41,43,44,47,49,51,

%T 53,55,59,61,62,63,65,67,69,71,73,74,76,79,80,83,86,87,89,94,95,97,99,

%U 101,103,104,107,109,111,113,116,118,119,122,123,124

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

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

%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="/A070087/b070087.txt">Table of n, a(n) for n=1..1000</a>

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

%t With[{lpfn=Table[FactorInteger[n][[-1,1]],{n,200}]},Flatten[ Position[ Partition[ lpfn,2,1],_?(#[[1]]>#[[2]]&),{1},Heads->False]]] (* _Harvey P. Dale_, Sep 14 2014 *)

%Y Cf. A006530, A070089.

%K nonn

%O 1,1

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

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Last modified January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)