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A082419 Numbers n such that P(n+2) < P(n) < P(n+1), where P(n) = largest prime factor of n (A006530). 1

%I

%S 6,10,22,25,28,30,33,46,52,58,68,70,78,82,88,93,98,102,106,110,115,

%T 126,130,133,138,141,145,148,160,166,172,178,187,190,198,201,205,208,

%U 213,222,226,232,236,238,248,253,262,268,273,286,292,304,306,310,316,328,346,348

%N Numbers n such that P(n+2) < P(n) < P(n+1), where P(n) = largest prime factor of n (A006530).

%D Antal Balog, On the largest prime factor of consecutive integers, Abstracts Amer. Math. Soc., 25 (No. 2, 2002), p. 337, #975-11-76.

%H T. D. Noe, <a href="/A082419/b082419.txt">Table of n, a(n) for n = 1..1000</a>

%H P. Erdős and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper17.pdf">On the largest prime factors of n and n+1</a>, Aequationes Math. 17 (1978), p. 311-321. [<a href="http://www.renyi.hu/~p_erdos/1978-29.pdf">alternate link</a>]

%t pflist=Select[Partition[Table[{n,lpf[n]},{n,400}],3,1],#[[3,-1]]< #[[1,-1]]< #[[2,-1]]&]; Table[pflist[[n,1,1]],{n,Length[pflist]}] (* _Harvey P. Dale_, Oct 25 2011 *)

%Y Cf. A006530, A082417-A082422, A071869, A071870.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 25 2003

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Last modified November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)