A229998 - OEIS

%I #11 Jun 16 2018 18:34:44

%S 1,2,3,4,5,3,7,8,9,1,11,6,13,7,3,16,17,9,19,10,21,11,23,12,25,13,27,

%T 14,29,3,31,32,33,17,7,18,37,19,39,4,41,21,43,22,45,23,47,24,49,5,51,

%U 26,53,27,55,28,57,29,59,3,61,31,63,64,1,33,67,2,69,7

%N Denominator of  d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1), where d(1),d(2),...,d(k) are the unitary divisors of n.

%e n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 5;

%e n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 3.

%e The first 10 sums:  1/1, 5/2, 10/3, 17/4, 26/5, 25/3, 50/7, 65/8, 82/9, 13/1.

%t r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; Table[r[n], {n, 1, 30}]; 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 = Table[Plus @@ t[n], {n, 1, 60}]; Numerator[u]   (* A229997 *)

%t Denominator[u] (* A229998 *)

%Y Cf. A229997.

%K nonn,easy,frac

%O 1,2

%A _Clark Kimberling_, Oct 31 2013

%E Definition corrected by _Clark Kimberling_, Jun 16 2018