A113645 Numbers k such that sum of exponents in prime factorization of k (i.e., A001222(k)) is >= each prime divisor of k.

4, 8, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 80, 81, 96, 108, 120, 128, 144, 160, 162, 180, 192, 200, 216, 240, 243, 256, 270, 288, 300, 320, 324, 360, 384, 400, 405, 432, 448, 450, 480, 486, 500, 512, 540, 576, 600, 640, 648, 672, 675, 720, 729, 750, 768

Offset: 1

Author

Leroy Quet, Jan 15 2006

Keywords

• nonn

Examples

			12 = 2^2 *3^1. Since the sum of the prime factorization exponents, 2+1 = 3, is >= the largest prime dividing 12, which is 3, then 12 is included in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

A proper subset of A068936.

Cf. A001222, A006530.

Programs

Mathematica

fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Max[First /@ f]]; Select[ Range[2, 800], fQ@ # &] (* Robert G. Wilson v, Jan 16 2006 *)
qu[n_]:=n>1&&Block[{f=Transpose@FactorInteger@n, s}, s=Plus@@f[[2]];s>=Max@f[[1]]]; L ={};Do[If[qu[n], Print[n];AppendTo[L, n]], {n, 1000}];L (* Giovanni Resta, Jan 16 2006 *)

PARI

isok(m) = {my(f=factor(m)); #select(x->(x>bigomega(f)), f[,1]~) == 0;} \\ Michel Marcus, Sep 17 2020

Formula

A number k is included if A006530(k) <= A001222(k).

Extensions

More terms from Robert G. Wilson v and Giovanni Resta, Jan 16 2006