A211273 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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}]

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: A376284 A285207 A140398 * A344988 A255774 A364005

Adjacent sequences: A211270 A211271 A211272 * A211274 A211275 A211276

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 07 2012

STATUS

approved