A274436 Numbers having fewer distinct prime factors of form 3*k+1 than of the form 3*k+2.

2, 4, 5, 6, 8, 10, 11, 12, 15, 16, 17, 18, 20, 22, 23, 24, 25, 29, 30, 32, 33, 34, 36, 40, 41, 44, 45, 46, 47, 48, 50, 51, 53, 54, 55, 58, 59, 60, 64, 66, 68, 69, 70, 71, 72, 75, 80, 82, 83, 85, 87, 88, 89, 90, 92, 94, 96, 99, 100, 101, 102, 106, 107, 108

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

18 = 2^1 3^2, so that the number of distinct primes 3*k+1 is 0 and the number of distinct primes 3*k + 2 is 1.

Mathematica

g[n_] := Map[First, FactorInteger[n]] ; z = 5000;
p1 = Select[Prime[Range[z]], Mod[#, 3] == 1 &];
p2 = Select[Prime[Range[z]], Mod[#, 3] == 2 &];
q1[n_] := Length[Intersection[g[n], p1]]
q2[n_] := Length[Intersection[g[n], p2]]
Select[Range[z], q1[#] == q2[#] &]; (* A274435 *)
Select[Range[z], q1[#] < q2[#] &]; (* A274436 *)
Select[Range[z], q1[#] > q2[#] &]; (* A274437 *)

Crossrefs

Cf. A274435, A274437.

Sequence in context: A047262 A361233 A285143 * A330330 A189796 A284818

Adjacent sequences: A274433 A274434 A274435 * A274437 A274438 A274439

Keyword

nonn,easy

Author

Clark Kimberling, Jul 19 2016

Status

approved