A306012 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 denominator of S(m) when all the numbers S(m) are arranged in increasing order.

1, 2, 3, 4, 5, 7, 8, 3, 9, 11, 1, 13, 6, 16, 17, 3, 7, 19, 10, 9, 23, 21, 25, 27, 12, 11, 29, 14, 31, 32, 13, 33, 37, 7, 18, 41, 4, 17, 43, 3, 39, 47, 22, 45, 19, 49, 53, 24, 26, 51, 23, 55, 28, 59, 21, 61, 5, 57, 64, 63, 67, 27, 1, 71, 2, 29, 73, 3, 36, 69

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 denominators are 1,2,3,4,5,7,8,3.
		

Crossrefs

Cf. A077610, A229994, A229996, A305995, A306010, A306011.

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 *)