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A137266 a(n) = number of positive integers k where k divides (n - floor(n/k)). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A096258 A049879

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

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Last modified June 1 13:20 EDT 2020. Contains 334762 sequences. (Running on oeis4.)