%I #14 Sep 27 2016 06:14:53
%S 1,2,2,4,3,5,5,6,6,8,6,10,9,9,9,13,11,12,12,14,14,16,12,18,17,17,17,
%T 19,17,21,21,22,20,22,20,26,26,24,22,28,25,29,27,29,29,29,27,33,33,32,
%U 32,36,30,34,34,38,38,38,34,40,39,39,37,43,41,45,43,41,41,45,43,50,48
%N a(n) = Sum_{k=1..n} floor(n/k + 1)-floor(n/k + 1/2).
%F Conjecture: Let f(a,b)=1, if (a+b) mod |a-b| != (a mod |a-b|)+(b mod |a-b|), and 0 otherwise. a(n) = Sum_{k=1..n-1} 1-f(n,k). - _Benedict W. J. Irwin_, Sep 22 2016
%e [4/1+1]-[4/1+1/2] + [4/2+1]-[4/2+1/2] + [4/3+1]-[4/3+1/2] + [4/4+1]-[4/4+1/2] = 1+1+1+1 = 4.
%t Table[Sum[Floor[n/k + 1] - Floor[n/k + 1/2], {k, n}], {n, 73}] (* _Michael De Vlieger_, Sep 26 2016 *)
%o (PARI) a(n) = sum(k=1, n, floor(n/k + 1)-floor(n/k + 1/2)); \\ _Michel Marcus_, Sep 24 2016
%K nonn
%O 1,2
%A _Clark Kimberling_, Oct 18 2002
%E Duplicate term at a(44) removed by _Benedict W. J. Irwin_, Sep 22 2016