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A274437
Numbers having more distinct prime factors of form 3*k+1 than of the form 3*k+2.
3
7, 13, 19, 21, 31, 37, 39, 43, 49, 57, 61, 63, 67, 73, 79, 91, 93, 97, 103, 109, 111, 117, 127, 129, 133, 139, 147, 151, 157, 163, 169, 171, 181, 182, 183, 189, 193, 199, 201, 211, 217, 219, 223, 229, 237, 241, 247, 259, 266, 271, 273, 277, 279, 283, 291
OFFSET
1,1
COMMENTS
Contains all terms of A004611 except 1. - Robert Israel, Aug 03 2016
LINKS
EXAMPLE
39 = 3^1 13^1, so that the number of distinct primes 3*k+1 is 1 and the number of distinct primes 3*k + 2 is 0.
MAPLE
filter:= proc(n) local P1, P2;
P1, P2:= selectremove(t -> t mod 3 = 1, numtheory:-factorset(n));
nops(P1) > nops(P2 minus {3})
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 03 2016
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 19 2016
STATUS
approved