A089341 Numbers k with lpf(k) < gpf(k) < 2*lpf(k), where lpf = A020639, gpf = A006530.

6, 12, 15, 18, 24, 35, 36, 45, 48, 54, 72, 75, 77, 91, 96, 108, 135, 143, 144, 162, 175, 187, 192, 209, 216, 221, 225, 245, 247, 288, 299, 323, 324, 375, 384, 391, 405, 432, 437, 486, 493, 527, 539, 551, 576, 589, 637, 648, 667, 675, 703, 713, 768, 847, 851

Offset: 1

Author

Reinhard Zumkeller, Jan 03 2004

Keywords

• nonn

Comments

A081306 without prime powers.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Smooth Number.

Crossrefs

Cf. A005279, A006530, A020639, A046665, A081306.

Subsequence of A024619.

Programs

Haskell

a089341 n = a089341_list !! (n-1)
a089341_list = filter (\x -> a006530 x < 2 * a020639 x) a024619_list
-- Reinhard Zumkeller, Sep 29 2014

Mathematica

q[k_] := Module[{p = FactorInteger[k][[;;, 1]]}, Length[p] > 1 && p[[-1]] < 2*p[[1]]]; Select[Range[1000], q] (* Amiram Eldar, May 16 2025 *)

PARI

isok(k) = if(k == 1, 0, my(p = factor(k)[,1], np = #p);  np > 1 && p[np] < 2*p[1]); \\ Amiram Eldar, May 16 2025

Formula

A046665(a(n)) < A020639(a(n)).