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A317243 a(n) is the number of open intervals (m, m+1) containing at least one fraction n/k, where m and k are integers between 1 and n. 0
0, 0, 1, 1, 2, 1, 3, 2, 3, 3, 4, 2, 5, 4, 4, 4, 6, 4, 6, 4, 6, 6, 7, 4, 7, 7, 7, 6, 8, 5, 9, 7, 8, 8, 8, 6, 10, 9, 9, 7, 10, 7, 11, 9, 9, 10, 11, 7, 11, 10, 11, 10, 12, 9, 11, 9, 12, 12, 13, 8, 13, 12, 11, 11, 13, 11, 14, 12, 13, 11, 14, 9, 15, 14, 13, 13, 14, 12, 15, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) is the number of distinct values floor(n/k) can take, for k an integer between 1 and n that does not divide n.

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

Fractions with 9 as the numerator, with a denominator not greater than the numerator, and that do not yield an integer, are:

9/2 that lies between 4 and 5,

9/4 between 2 and 3,

9/5, 9/6, 9/7, 9/8 between 1 and 2.

Three intervals are involved, so a(9)=3.

MATHEMATICA

a[n_] := Length[ Union[Floor /@ Select[n/# & /@ Range[n], ! IntegerQ[#] &]]]; Array[a, 80]

CROSSREFS

Cf. A055086 (when k is allowed to divide n).

Cf. A316519 (when frac(n/k) is used instead of floor(n/k)).

Sequence in context: A253281 A029206 A029200 * A051274 A267806 A025797

Adjacent sequences:  A317240 A317241 A317242 * A317244 A317245 A317246

KEYWORD

nonn

AUTHOR

Luc Rousseau, Jul 24 2018

STATUS

approved

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Last modified September 25 14:37 EDT 2021. Contains 347654 sequences. (Running on oeis4.)