OFFSET
1,2
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
35 = 5^1 7^1, in which the number of distinct primes 6*k+1 is 1 and the number of distinct primes 6*k + 5 is 1.
MAPLE
N:= 1000: # to get all terms <= N
filter:= proc(n)
local P1, P5;
P1, P5:= selectremove(t -> t mod 6 = 1, numtheory:-factorset(n) minus {2, 3});
nops(P1)=nops(P5)
end proc:
sort(map(t -> seq(t*2^j, j=0..ilog2(N/t)),
select(filter, [seq(i, i=1..N, 2)]))); # Robert Israel, Jul 20 2016
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 20 2016
STATUS
approved