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A229997 Numerator 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.

%I A229997 #13 Jun 16 2018 18:34:36
%S A229997 1,5,10,17,26,25,50,65,82,13,122,85,170,125,52,257,290,205,362,221,
%T A229997 500,305,530,325,626,425,730,425,842,130,962,1025,1220,725,260,697,
%U A229997 1370,905,1700,169,1682,1250,1850,1037,2132,1325,2210,1285,2402,313,2900
%N A229997 Numerator 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 A229997 n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 26;
%e A229997 n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 25.
%e A229997 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 A229997 r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; Table[
%t A229997 r[n], {n, 1, 30}]; k[n_] := Length[r[n]];
%t A229997 t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}]
%t A229997 u = Table[Plus @@ t[n], {n, 1, 60}]; Numerator[u]  (* A229997 *)
%t A229997 Denominator[u] (* A229998 *)
%Y A229997 Cf. A229998, A229999.
%K A229997 nonn,easy,frac
%O A229997 1,2
%A A229997 _Clark Kimberling_, Oct 31 2013
%E A229997 Definition corrected by _Clark Kimberling_, Jun 16 2018