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A306011 Let S(m) = d(k)/d(1) + ... + d(1)/d(k), where d(1)..d(k) are the unitary divisors of m; then a(n) is the numerator of S(m) when all the numbers S(m) are arranged in increasing order.

%I A306011 #12 Jun 25 2024 01:30:00
%S A306011 1,5,10,17,26,50,65,25,82,122,13,170,85,257,290,52,125,362,221,205,
%T A306011 530,500,626,730,325,305,842,425,962,1025,425,1220,1370,260,697,1682,
%U A306011 169,725,1850,130,1700,2210,1037,2132,905,2402,2810,1285,1445,2900,1325
%N A306011 Let S(m) = d(k)/d(1) + ... + d(1)/d(k), where d(1)..d(k) are the unitary divisors of m; then a(n) is the numerator of S(m) when all the numbers S(m) are arranged in increasing order.
%e A306011 The first 8 pairs {m,S(m)} are {1, 1}, {2, 5/2}, {3, 10/3}, {4, 17/4}, {5, 26/5}, {6, 25/3}, {7, 50/7}, {8, 65/8}. When the numbers S(m) are arranged in increasing order, the pairs are {1, 1}, {2, 5/2}, {3, 10/3}, {4, 17/4}, {5, 26/5}, {7, 50/7}, {8, 65/8}, {6, 25/3}, so that the first 8 numerators are 1,5,10,17,26,50,65,25.
%t A306011 z = 100; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &];
%t A306011 k[n_] := Length[r[n]];
%t A306011 t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];
%t A306011 s = Table[{n, Total[t[n]]}, {n, 1, z}]
%t A306011 v = SortBy[s, Last]
%t A306011 v1 = Table[v[[n]][[1]], {n, 1, z}]  (* A306010 *)
%t A306011 w = Table[v[[n]][[2]], {n, 1, z}];
%t A306011 Numerator[w]    (* A306011 *)
%t A306011 Denominator[w]  (* A306012 *)
%Y A306011 Cf. A077610, A229994, A229996, A305995, A306010, A306012.
%K A306011 nonn
%O A306011 1,2
%A A306011 _Clark Kimberling_, Jun 16 2018