A275200 Numbers having fewer distinct prime factors of form 6*k+1 than of the form 6*k+5.

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

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 A351327

Adjacent sequences: A275197 A275198 A275199 * A275201 A275202 A275203

Keyword

nonn,easy

Author

Clark Kimberling, Jul 20 2016

Status

approved