A229998 Denominator of d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1), where d(1),d(2),...,d(k) are the unitary divisors of n.

1, 2, 3, 4, 5, 3, 7, 8, 9, 1, 11, 6, 13, 7, 3, 16, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 3, 31, 32, 33, 17, 7, 18, 37, 19, 39, 4, 41, 21, 43, 22, 45, 23, 47, 24, 49, 5, 51, 26, 53, 27, 55, 28, 57, 29, 59, 3, 61, 31, 63, 64, 1, 33, 67, 2, 69, 7

Offset: 1

Author

Clark Kimberling, Oct 31 2013

Keywords

• nonn
• easy
• frac

Examples

			n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 5;
n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 3.
The first 10 sums:  1/1, 5/2, 10/3, 17/4, 26/5, 25/3, 50/7, 65/8, 82/9, 13/1.
		

Crossrefs

Cf. A229997.

Programs

Mathematica

r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; Table[r[n], {n, 1, 30}]; k[n_] := Length[r[n]]; t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}]; u = Table[Plus @@ t[n], {n, 1, 60}]; Numerator[u]   (* A229997 *)
Denominator[u] (* A229998 *)

Extensions

Definition corrected by Clark Kimberling, Jun 16 2018