A306010 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 number m when the sums S(m) are arranged in increasing order.

1, 2, 3, 4, 5, 7, 8, 6, 9, 11, 10, 13, 12, 16, 17, 15, 14, 19, 20, 18, 23, 21, 25, 27, 24, 22, 29, 28, 31, 32, 26, 33, 37, 35, 36, 41, 40, 34, 43, 30, 39, 47, 44, 45, 38, 49, 53, 48, 52, 51, 46, 55, 56, 59, 42, 61, 50, 57, 64, 63, 67, 54, 65, 71, 68, 58, 73

Offset: 1

Author

Clark Kimberling, Jun 16 2018

Keywords

• nonn

Comments

This is a permutation of the positive integers.

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 terms of (a(n)) are 1,2,3,4,5,7,8,6.
		

Crossrefs

Cf. A077610, A229994, A229996, A305995, A306011, 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 *)