cp's OEIS Frontend

A075988 Number of integers k satisfying 1 <= k <= n and 0 < frac(n/k) < 1/2, where frac(n/k) is the fractional part of n/k; i.e., frac(n/k) = n/k - floor(n,k).

%I A075988 #14 Sep 08 2022 08:45:07
%S A075988 0,0,0,1,1,1,3,2,3,4,4,4,7,5,5,8,9,6,10,8,10,12,10,10,14,13,13,13,15,
%T A075988 13,19,16,16,18,16,17,24,20,18,20,23,21,25,23,23,25,25,23,30,26,28,30,
%U A075988 28,26,30,30,34,34,32,28,37,35,31,36,37,37,41,35,37,37,41,38,46,42,40
%N A075988 Number of integers k satisfying 1 <= k <= n and 0 < frac(n/k) < 1/2, where frac(n/k) is the fractional part of n/k; i.e., frac(n/k) = n/k - floor(n,k).
%F A075988 Sum_{k=1..n} (ceiling(n/k) - round(n/k)). - _Vladeta Jovovic_, Mar 01 2004
%o A075988 (Magma) [&+[(Ceiling(n/k)-Round(n/k)): k in [1..n]]: n in [1..80]]; // _Vincenzo Librandi_, Jul 30 2017
%o A075988 (PARI) a(n) = sum(k=1, n, f = frac(n/k); f  && (f < 1/2)); \\ _Michel Marcus_, Jul 30 2017
%Y A075988 Cf. A075989, A076990.
%K A075988 nonn
%O A075988 1,7
%A A075988 _Clark Kimberling_, Sep 28 2002