A232724 Numbers k satisfying g(k - g(k)) > g(k) = greatest prime divisor of k.

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

Author

Clark Kimberling, Dec 11 2013

Keywords

• nonn
• easy

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.

Examples

			g(18) = 3, g(18-3) = g(15) = 5, and 18 is the 3rd positive integer having the defining property, so a(3) = 18.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1502

Crossrefs

Cf. A233341, A233342, A006530, A000040.

Programs

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