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

1,1

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

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

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

Cf. A233341, A233342, A006530, A000040.

Sequence in context: A140270 A257225 A092456 * A260409 A257509 A232570

Adjacent sequences: A232721 A232722 A232723 * A232725 A232726 A232727

Keyword

nonn,easy

Author

Clark Kimberling, Dec 11 2013

Status

approved