OFFSET
1,2
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
76 = 2^2 * 19^1, so that the number of distinct primes of the form 3*k+1 is 1 and the number of distinct primes of the form 3*k+2 is 1.
3 and 9 are also terms, since they have no prime factors of either type.
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 *)
PROG
(PARI) is(n) = my(f=factor(n)[, 1]~, i=0, j=0); for(k=1, #f, if(!((f[k]-1)%3), i++); if(!((f[k]-2)%3), j++)); i==j \\ Felix Fröhlich, Jul 09 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 19 2016
STATUS
approved