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).

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, 13, 19, 16, 16, 18, 16, 17, 24, 20, 18, 20, 23, 21, 25, 23, 23, 25, 25, 23, 30, 26, 28, 30, 28, 26, 30, 30, 34, 34, 32, 28, 37, 35, 31, 36, 37, 37, 41, 35, 37, 37, 41, 38, 46, 42, 40

Offset

1,7

Links

Table of n, a(n) for n=1..75.

Formula

Sum_{k=1..n} (ceiling(n/k) - round(n/k)). - Vladeta Jovovic, Mar 01 2004

Prog

(Magma) [&+[(Ceiling(n/k)-Round(n/k)): k in [1..n]]: n in [1..80]]; // Vincenzo Librandi, Jul 30 2017
(PARI) a(n) = sum(k=1, n, f = frac(n/k); f  && (f < 1/2)); \\ Michel Marcus, Jul 30 2017

Crossrefs

Cf. A075989, A076990.

Sequence in context: A098822 A131597 A077070 * A029150 A255246 A055923

Adjacent sequences: A075985 A075986 A075987 * A075989 A075990 A075991

Keyword

nonn

Author

Clark Kimberling, Sep 28 2002

Status

approved