

A275200


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


3



5, 10, 11, 15, 17, 20, 22, 23, 25, 29, 30, 33, 34, 40, 41, 44, 45, 46, 47, 50, 51, 53, 55, 58, 59, 60, 66, 68, 69, 71, 75, 80, 82, 83, 85, 87, 88, 89, 90, 92, 94, 99, 100, 101, 102, 106, 107, 110, 113, 115, 116, 118, 120, 121, 123, 125, 131, 132, 135, 136
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OFFSET

1,1


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000


EXAMPLE

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.


MATHEMATICA

g[n_] := Map[First, FactorInteger[n]];
p1 = Select[Prime[Range[200]], Mod[#, 6] == 1 &];
p2 = Select[Prime[Range[200]], Mod[#, 6] == 5 &];
q1[n_] := Length[Intersection[g[n], p1]]
q2[n_] := Length[Intersection[g[n], p2]]
Select[Range[200], q1[#] == q2[#] &] (* A275199 *)
Select[Range[200], q1[#] < q2[#] &] (* A275200 *)
Select[Range[200], q1[#] > q2[#] &] (* A275201 *)


CROSSREFS

Cf. A275199, A275201.
Sequence in context: A296699 A297132 A136823 * A225838 A036788 A136811
Adjacent sequences: A275197 A275198 A275199 * A275201 A275202 A275203


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 20 2016


STATUS

approved



