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

1,2

Comments

This is a permutation of the positive integers.

Links

Table of n, a(n) for n=1..67.

Example

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.

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 *)

Crossrefs

Cf. A077610, A229994, A229996, A305995, A306011, A306012.

Sequence in context: A130994 A266405 A295087 * A162375 A370793 A334100

Adjacent sequences: A306007 A306008 A306009 * A306011 A306012 A306013

Keyword

nonn

Author

Clark Kimberling, Jun 16 2018

Status

approved