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Numbers having fewer distinct prime factors of form 6*k+1 than of the form 6*k+5.
3

%I #4 Jul 22 2016 22:09:23

%S 5,10,11,15,17,20,22,23,25,29,30,33,34,40,41,44,45,46,47,50,51,53,55,

%T 58,59,60,66,68,69,71,75,80,82,83,85,87,88,89,90,92,94,99,100,101,102,

%U 106,107,110,113,115,116,118,120,121,123,125,131,132,135,136

%N Numbers having fewer distinct prime factors of form 6*k+1 than of the form 6*k+5.

%H Clark Kimberling, <a href="/A275200/b275200.txt">Table of n, a(n) for n = 1..1000</a>

%e 30 = 2^1 3^1 5^1 , so that the number of distinct primes 6*k+1 is 0 and the number of distinct primes 6*k + 5 is 1.

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

%t p1 = Select[Prime[Range[200]], Mod[#, 6] == 1 &];

%t p2 = Select[Prime[Range[200]], Mod[#, 6] == 5 &];

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

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

%t Select[Range[200], q1[#] == q2[#] &] (* A275199 *)

%t Select[Range[200], q1[#] < q2[#] &] (* A275200 *)

%t Select[Range[200], q1[#] > q2[#] &] (* A275201 *)

%Y Cf. A275199, A275201.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 20 2016