A229994 - OEIS

%I #15 Mar 21 2020 04:06:21

%S 1,2,1,3,1,4,1,5,1,6,3,2,1,7,1,8,1,9,1,10,5,2,1,11,1,12,4,3,1,13,1,14,

%T 7,2,1,15,5,3,1,16,1,17,1,18,9,2,1,19,1,20,5,4,1,21,7,3,1,22,11,2,1,

%U 23,1,24,8,3,1,25,1,26,13,2,1,27,1,28,7,4,1

%N For every positive integer m, let u(m) = (d(1),d(2),...,d(k)) be the unitary divisors of m in increasing order. Let Q be the concatenation of the vectors (d(k)/d(1), d(k-1)/d(2), ..., d(1)/d(k)), so that every positive rational number appears in Q exactly once. The numerators form A229994; the denominators, A077610.

%C The number of terms in S(m) is A034444(m); the denominators are given by A077610.

%H Clark Kimberling, <a href="/A229994/b229994.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Ra#rational">Index entries for sequences related to enumerating the rationals</a>

%e The first fifteen positive rationals:  1, 2, 1/2, 3, 1/3, 4, 1/4, 5, 1/5, 6, 3/2, 2/3, 1/6, 7, 1/7.

%t z = 40; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; k[n_] := Length[r[n]]; t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}]; u[1] = t[1]; u[n_] := Join[u[n - 1], t[n]];

%t Numerator[u[z]]   (* A229994 *)

%t Denominator[u[z]] (* A077610 *)

%Y Cf. A077610, A229996.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Oct 31 2013

%E Definition corrected by _Clark Kimberling_, Jun 16 2018