

A232724


a(n) = nth number 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
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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(183) = 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



