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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 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.)