cp's OEIS Frontend

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.

%I A306010 #11 Feb 06 2019 11:42:17
%S A306010 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,
%T A306010 29,28,31,32,26,33,37,35,36,41,40,34,43,30,39,47,44,45,38,49,53,48,52,
%U A306010 51,46,55,56,59,42,61,50,57,64,63,67,54,65,71,68,58,73
%N 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.
%C A306010 This is a permutation of the positive integers.
%e A306010 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.
%t A306010 z = 100; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &];
%t A306010 k[n_] := Length[r[n]];
%t A306010 t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];
%t A306010 s = Table[{n, Total[t[n]]}, {n, 1, z}]
%t A306010 v = SortBy[s, Last]
%t A306010 v1 = Table[v[[n]][[1]], {n, 1, z}]  (* A306010 *)
%t A306010 w = Table[v[[n]][[2]], {n, 1, z}];
%t A306010 Numerator[w]    (* A306011 *)
%t A306010 Denominator[w]  (* A306012 *)
%Y A306010 Cf. A077610, A229994, A229996, A305995, A306011, A306012.
%K A306010 nonn
%O A306010 1,2
%A A306010 _Clark Kimberling_, Jun 16 2018