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 A275201 Numbers having more distinct prime factors of form 6*k+1 than of the form 6*k+5. 3

%I

%S 7,13,14,19,21,26,28,31,37,38,39,42,43,49,52,56,57,61,62,63,67,73,74,

%T 76,78,79,84,86,91,93,97,98,103,104,109,111,112,114,117,122,124,126,

%U 127,129,133,134,139,146,147,148,151,152,156,157,158,163,168,169

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

%H Clark Kimberling, <a href="/A275201/b275201.txt">Table of n, a(n) for n = 1..1000</a>

%e 56 = 2^3 7^1, so that the number of distinct primes 6*k+1 is 1 and the number of distinct primes 6*k + 5 is 0.

%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, A275200.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 20 2016

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Last modified June 5 09:58 EDT 2020. Contains 334840 sequences. (Running on oeis4.)