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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). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

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

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 *)

CROSSREFS

Cf. A229994, A229996.

Sequence in context: A137720 A199896 A213355 * A258618 A093119 A239538

Adjacent sequences:  A229996 A229997 A229998 * A230000 A230001 A230002

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 31 2013

EXTENSIONS

Definition corrected by Clark Kimberling, Jun 16 2018

STATUS

approved

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Last modified January 24 22:45 EST 2022. Contains 350565 sequences. (Running on oeis4.)