A211273 Number of integer pairs (x,y) such that 0<x<=y<=n and x*y<=2n.

0, 2, 5, 7, 10, 13, 15, 19, 22, 25, 28, 32, 35, 39, 43, 46, 49, 55, 57, 62, 66, 69, 73, 78, 82, 86, 90, 95, 98, 104, 106, 112, 117, 120, 125, 131, 133, 138, 143, 148, 152, 158, 161, 166, 172, 176, 179, 186, 189, 196, 200, 204, 209, 215, 219, 225, 229, 233

Offset

1,2

Comments

For a guide to related sequences, see A211266.

Links

Table of n, a(n) for n=1..58.

Example

a(5) counts these pairs: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3)

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 *)

Crossrefs

Cf. A211266.

Sequence in context: A047480 A285207 A140398 * A344988 A255774 A364005

Adjacent sequences: A211270 A211271 A211272 * A211274 A211275 A211276

Keyword

nonn

Author

Clark Kimberling, Apr 07 2012

Status

approved