A229997 Numerator 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, 5, 10, 17, 26, 25, 50, 65, 82, 13, 122, 85, 170, 125, 52, 257, 290, 205, 362, 221, 500, 305, 530, 325, 626, 425, 730, 425, 842, 130, 962, 1025, 1220, 725, 260, 697, 1370, 905, 1700, 169, 1682, 1250, 1850, 1037, 2132, 1325, 2210, 1285, 2402, 313, 2900

Offset

1,2

Links

Table of n, a(n) for n=1..51.

Example

n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 26;
n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 25.
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. A229998, A229999.

Sequence in context: A105705 A061409 A342553 * A277186 A193053 A340047

Adjacent sequences: A229994 A229995 A229996 * A229998 A229999 A230000

Keyword

nonn,easy,frac

Author

Clark Kimberling, Oct 31 2013

Extensions

Definition corrected by Clark Kimberling, Jun 16 2018

Status

approved