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.

1, 5, 10, 17, 26, 50, 65, 25, 82, 122, 13, 170, 85, 257, 290, 52, 125, 362, 221, 205, 530, 500, 626, 730, 325, 305, 842, 425, 962, 1025, 425, 1220, 1370, 260, 697, 1682, 169, 725, 1850, 130, 1700, 2210, 1037, 2132, 905, 2402, 2810, 1285, 1445, 2900, 1325

Offset: 1

Author

Clark Kimberling, Jun 16 2018

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A077610, A229994, A229996, A305995, A306010, A306012.

Programs

Mathematica

z = 100; 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]}];
s = Table[{n, Total[t[n]]}, {n, 1, z}]
v = SortBy[s, Last]
v1 = Table[v[[n]][[1]], {n, 1, z}]  (* A306010 *)
w = Table[v[[n]][[2]], {n, 1, z}];
Numerator[w]    (* A306011 *)
Denominator[w]  (* A306012 *)