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

7, 13, 14, 19, 21, 26, 28, 31, 37, 38, 39, 42, 43, 49, 52, 56, 57, 61, 62, 63, 67, 73, 74, 76, 78, 79, 84, 86, 91, 93, 97, 98, 103, 104, 109, 111, 112, 114, 117, 122, 124, 126, 127, 129, 133, 134, 139, 146, 147, 148, 151, 152, 156, 157, 158, 163, 168, 169

Offset

1,1

Links

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

Example

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.

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, A275200.

Sequence in context: A050931 A072864 A232437 * A274558 A120100 A308525

Adjacent sequences: A275198 A275199 A275200 * A275202 A275203 A275204

Keyword

nonn,easy

Author

Clark Kimberling, Jul 20 2016

Status

approved