%I #8 Aug 03 2016 15:59:39

%S 7,13,19,21,31,37,39,43,49,57,61,63,67,73,79,91,93,97,103,109,111,117,

%T 127,129,133,139,147,151,157,163,169,171,181,182,183,189,193,199,201,

%U 211,217,219,223,229,237,241,247,259,266,271,273,277,279,283,291

%N Numbers having more distinct prime factors of form 3*k+1 than of the form 3*k+2.

%C Contains all terms of A004611 except 1. - _Robert Israel_, Aug 03 2016

%H Clark Kimberling, <a href="/A274437/b274437.txt">Table of n, a(n) for n = 1..10000</a>

%e 39 = 3^1 13^1, so that the number of distinct primes 3*k+1 is 1 and the number of distinct primes 3*k + 2 is 0.

%p filter:= proc(n) local P1,P2;

%p P1,P2:= selectremove(t -> t mod 3 = 1, numtheory:-factorset(n));

%p nops(P1) > nops(P2 minus {3})

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Aug 03 2016

%t g[n_] := Map[First, FactorInteger[n]] ; z = 5000;

%t p1 = Select[Prime[Range[z]], Mod[#, 3] == 1 &];

%t p2 = Select[Prime[Range[z]], Mod[#, 3] == 2 &];

%t q1[n_] := Length[Intersection[g[n], p1]]

%t q2[n_] := Length[Intersection[g[n], p2]]

%t Select[Range[z], q1[#] == q2[#] &];(* A274435 *)

%t Select[Range[z], q1[#] < q2[#] &]; (* A274436 *)

%t Select[Range[z], q1[#] > q2[#] &]; (* A274437 *)

%Y Cf. A004611, A274435, A274436.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 19 2016