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%I #7 Jun 22 2021 01:05:59
%S 8,16,18,24,32,36,40,48,54,60,64,72,75,81,84,90,96,98,100,108,120,126,
%T 128,135,140,144,150,154,160,162,168,180,189,192,198,200,210,216,220,
%U 224,225,234,240,243,245,250,256,260,264,270,280,288,294,297,300
%N Numbers k satisfying g(k - g(k)) > g(k) = greatest prime divisor of k.
%C Conjecture: for every positive integer d, there exist infinitely many n for which a(n + 1) - a(n) + d; for d = 1, the first 4 such n are 40, 67, 76, 79.
%H Clark Kimberling, <a href="/A232724/b232724.txt">Table of n, a(n) for n = 1..1502</a>
%e g(18) = 3, g(18-3) = g(15) = 5, and 18 is the 3rd positive integer having the defining property, so a(3) = 18.
%t g[n_] := g[n] = FactorInteger[n][[-1, 1]]; t = {}; Do[If[g[n - g[n]] > g[n], AppendTo[t, n]], {n, 1, 500}]; t
%Y Cf. A233341, A233342, A006530, A000040.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Dec 11 2013
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