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
Keywords
Programs
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Magma
[&+[(Ceiling(n/k)-Round(n/k)): k in [1..n]]: n in [1..80]]; // Vincenzo Librandi, Jul 30 2017
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PARI
a(n) = sum(k=1, n, f = frac(n/k); f && (f < 1/2)); \\ Michel Marcus, Jul 30 2017
Formula
Sum_{k=1..n} (ceiling(n/k) - round(n/k)). - Vladeta Jovovic, Mar 01 2004