cp's OEIS Frontend

A229999 For every positive integer m, let u(m) = (d(1),d(2),...,d(k)) be the unitary divisors of m. The sequence (a(n)) consists of integers of the form d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1).

%I A229999 #12 Jun 16 2018 18:35:00
%S A229999 1,13,68,170,289,377,1160,2105,2900,4930,9425,10946,19594,20740,33680,
%T A229999 51850,45385,52625,69716,84200,83522,88145,107848,143140,269620,
%U A229999 208520,226577,273650,353800,458354,521300,540985,568226,884500,760328,832745,876265
%N A229999 For every positive integer m, let u(m) = (d(1),d(2),...,d(k)) be the unitary divisors of m. The sequence (a(n)) consists of integers of the form d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1).
%C A229999 The values of m for which d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1) is an integer are given by A229996. - _Clark Kimberling_, Jun 16 2018
%e A229999 a(2) = 13 = 10/1 + 5/2 + 2/5 + 1/10.
%t A229999 z = 10000; r[n_] := r[n] = Select[Divisors[n], GCD[#, n/#] == 1 &];
%t A229999 k[n_] := f[n] = Length[r[n]]; t[n_] := t[n] = Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}]; s = Table[Plus @@ t[n], {n, 1, z}]; a[n_] := a[n] = If[IntegerQ[s[[n]]], 1, 0]; u = Table[a[n], {n, 1, z}]; v = Flatten[Position[u, 1]]  (* A229996 *)
%t A229999 s[[v]] (* A229999 *)
%Y A229999 Cf. A229994, A229996.
%K A229999 nonn,easy
%O A229999 1,2
%A A229999 _Clark Kimberling_, Oct 31 2013
%E A229999 Definition corrected by _Clark Kimberling_, Jun 16 2018