A137266 a(n) = number of positive integers k where k divides (n - floor(n/k)).

1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 3, 4, 3, 3, 4, 5, 3, 5, 3, 4, 4, 4, 3, 6, 3, 5, 5, 5, 2, 4, 6, 6, 3, 3, 5, 8, 4, 3, 4, 7, 2, 5, 5, 6, 5, 3, 4, 8, 5, 6, 4, 5, 4, 6, 4, 6, 5, 5, 3, 8, 2, 5, 7, 8, 4, 5, 4, 6, 4, 5, 5, 9, 4, 5, 6, 6, 3, 5, 5, 9, 7, 4, 3, 8, 5, 4, 5, 6, 4, 8, 6, 5, 5, 4, 5, 9, 3, 6, 7, 10, 4, 5, 4, 6, 5

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Example

For n = 8, checking: 1 divides (8 - floor(8/1))=0. 2 divides (8 - floor(8/2))=4. 3 divides (8 - floor(8/3))=6. 4 doesn't divide (8 - floor(8/4))=6. 5 doesn't divide (8 - floor(8/5))=7. 6 doesn't divide (8 - floor(8/6))=7. 7 divides (8 - floor(8/7))=7. 8 doesn't divide (8 - floor(8/8))=7. For k > 8, k doesn't divide (n - floor(n/k)) = n. There are 4 cases where k does divide (n-floor(n/k)); so a(8) = 4.

Mathematica

Join[{1}, Table[Total[Table[If[Divisible[n-Floor[n/k], k], 1, 0], {k, n-1}]], {n, 2, 120}]] (* Harvey P. Dale, May 09 2020 *)

Crossrefs

Sequence in context: A109337 A303539 A303540 * A062948 A365159 A358639

Adjacent sequences: A137263 A137264 A137265 * A137267 A137268 A137269

Keyword

nonn

Author

Leroy Quet, Apr 26 2008

Extensions

More terms from R. J. Mathar, Feb 27 2009

Status

approved