A082417 - OEIS

A082417

Numbers k such that P(k) < P(k+1) > P(k+2), where P(k) is the largest prime factor of k (A006530).

%I #16 Jun 06 2022 05:47:19

%S 2,4,6,10,12,16,18,22,25,28,30,33,36,40,42,46,48,50,52,54,58,60,64,66,

%T 68,70,72,75,78,82,85,88,93,96,98,100,102,106,108,110,112,115,117,121,

%U 126,128,130,133,136,138,141,145,148,150,154,156,160,162,166,172,178,180,182

%N Numbers k such that P(k) < P(k+1) > P(k+2), where P(k) is the largest prime factor of k (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="/A082417/b082417.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>]

%F a(n) = A100392(n) - 1. - _T. D. Noe_, Nov 26 2007

%t gpf[n_] := FactorInteger[n][[-1, 1]]; ind = Position[Differences[Array[gpf, 200]], _?(# > 0 &)] // Flatten; ind[[Position[Differences[ind], _?(# > 1 &)] // Flatten]] (* _Amiram Eldar_, Jun 06 2022 *)

%Y Cf. A006530, A082418-A082422, A071869, A071870, A100392.

%K nonn

%O 1,1

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