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 A275199 Numbers having equal numbers of distinct prime factors of forms 6*k+1 and 6*k+5. 3
 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 35, 36, 48, 54, 64, 65, 70, 72, 77, 81, 95, 96, 105, 108, 119, 128, 130, 140, 143, 144, 154, 155, 161, 162, 175, 185, 190, 192, 195, 203, 209, 210, 215, 216, 221, 231, 238, 243, 245, 256, 260, 280, 285, 286, 287 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence and A275200 and A275201 partition the positive integers. 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 Cf. A275200, A275201. Sequence in context: A097755 A301704 A083854 * A003586 A114334 A262609 Adjacent sequences:  A275196 A275197 A275198 * A275200 A275201 A275202 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 20 2016 STATUS approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)