A211275 - OEIS

%I #6 Dec 21 2015 04:26:59

%S 0,1,1,2,2,3,3,5,5,6,6,8,8,9,9,11,11,13,13,15,15,16,16,19,19,20,20,22,

%T 22,24,24,27,27,28,28,31,31,32,32,35,35,37,37,39,39,40,40,44,44,46,46,

%U 48,48,50,50,53,53,54,54,58,58,59,59,62,62,64,64,66,66,68,68

%N Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= floor(n/2).

%C For a guide to related sequences, see A211266.

%t a = 1; b = n; z1 = 120;

%t t[n_] :=  t[n] = Flatten[Table[x*y, {x, a, b - 1},

%t {y, x, b}]]

%t c[n_, k_] := c[n, k] = Count[t[n], k]

%t Table[c[n, n], {n, 1, z1}]           (* A038548 *)

%t Table[c[n, n + 1], {n, 1, z1}]       (* A072670 *)

%t Table[c[n, 2*n], {n, 1, z1}]         (* A211270 *)

%t Table[c[n, 3*n], {n, 1, z1}]         (* A211271 *)

%t Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211272 *)

%t c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]

%t Print

%t Table[c1[n, n], {n, 1, z1}]          (* A094820 *)

%t Table[c1[n, n + 1], {n, 1, z1}]      (* A091627 *)

%t Table[c1[n, 2*n], {n, 1, z1}]        (* A211273 *)

%t Table[c1[n, 3*n], {n, 1, z1}]        (* A211274 *)

%t Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)

%Y Cf. A211266.

%K nonn

%O 1,4

%A _Clark Kimberling_, Apr 07 2012