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A232724
Numbers k satisfying g(k - g(k)) > g(k) = greatest prime divisor of k.
1
8, 16, 18, 24, 32, 36, 40, 48, 54, 60, 64, 72, 75, 81, 84, 90, 96, 98, 100, 108, 120, 126, 128, 135, 140, 144, 150, 154, 160, 162, 168, 180, 189, 192, 198, 200, 210, 216, 220, 224, 225, 234, 240, 243, 245, 250, 256, 260, 264, 270, 280, 288, 294, 297, 300
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
g(18) = 3, g(18-3) = g(15) = 5, and 18 is the 3rd positive integer having the defining property, so a(3) = 18.
MATHEMATICA
g[n_] := g[n] = FactorInteger[n][[-1, 1]]; t = {}; Do[If[g[n - g[n]] > g[n], AppendTo[t, n]], {n, 1, 500}]; t
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 11 2013
STATUS
approved