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.
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
KEYWORD
nonn
AUTHOR
Luc Rousseau, Jul 24 2018
STATUS
approved