A211275 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= floor(n/2).

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, 22, 24, 24, 27, 27, 28, 28, 31, 31, 32, 32, 35, 35, 37, 37, 39, 39, 40, 40, 44, 44, 46, 46, 48, 48, 50, 50, 53, 53, 54, 54, 58, 58, 59, 59, 62, 62, 64, 64, 66, 66, 68, 68

Offset: 1

Author

Clark Kimberling, Apr 07 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211266.

Crossrefs

Cf. A211266.

Programs

Mathematica

a = 1; b = n; z1 = 120;
t[n_] :=  t[n] = Flatten[Table[x*y, {x, a, b - 1},
{y, x, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 1, z1}]           (* A038548 *)
Table[c[n, n + 1], {n, 1, z1}]       (* A072670 *)
Table[c[n, 2*n], {n, 1, z1}]         (* A211270 *)
Table[c[n, 3*n], {n, 1, z1}]         (* A211271 *)
Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211272 *)
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Print
Table[c1[n, n], {n, 1, z1}]          (* A094820 *)
Table[c1[n, n + 1], {n, 1, z1}]      (* A091627 *)
Table[c1[n, 2*n], {n, 1, z1}]        (* A211273 *)
Table[c1[n, 3*n], {n, 1, z1}]        (* A211274 *)
Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)