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

1,2

Links

Table of n, a(n) for n=1..70.

Example

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.

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 *)

Crossrefs

Cf. A229997.

Sequence in context: A081810 A335791 A071829 * A331469 A067620 A343253

Adjacent sequences: A229995 A229996 A229997 * A229999 A230000 A230001

Keyword

nonn,easy,frac

Author

Clark Kimberling, Oct 31 2013

Extensions

Definition corrected by Clark Kimberling, Jun 16 2018

Status

approved