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).

1, 13, 68, 170, 289, 377, 1160, 2105, 2900, 4930, 9425, 10946, 19594, 20740, 33680, 51850, 45385, 52625, 69716, 84200, 83522, 88145, 107848, 143140, 269620, 208520, 226577, 273650, 353800, 458354, 521300, 540985, 568226, 884500, 760328, 832745, 876265

Offset: 1

Author

Clark Kimberling, Oct 31 2013

Keywords

• nonn
• easy

Comments

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

Examples

			a(2) = 13 = 10/1 + 5/2 + 2/5 + 1/10.
		

Crossrefs

Cf. A229994, A229996.

Programs

Mathematica

z = 10000; r[n_] := r[n] = Select[Divisors[n], GCD[#, n/#] == 1 &];
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 *)
s[[v]] (* A229999 *)

Extensions

Definition corrected by Clark Kimberling, Jun 16 2018