A211266 Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=2n.

0, 1, 3, 5, 7, 10, 12, 15, 18, 21, 24, 28, 30, 34, 38, 41, 44, 49, 51, 56, 60, 63, 67, 72, 75, 79, 83, 88, 91, 97, 99, 104, 109, 112, 117, 123, 125, 130, 135, 140, 143, 149, 152, 157, 163, 167, 170, 177, 180, 186, 190, 194, 199, 205, 209, 215, 219, 223

Offset

1,3

Comments

Guide to related sequences:

A056924 ... 1<=x<y<=n .... x*y=n

A211159 ... 1<=x<y<=n .... x*y=n+1

A211261 ... 1<=x<y<=n .... x*y=2n

A211262 ... 1<=x<y<=n .... x*y=3n

A211263 ... 1<=x<y<=n .... x*y=floor(n/2)

A211264 ... 1<=x<y<=n .... x*y<=n

A211265 ... 1<=x<y<=n .... x*y<=n+1

A211266 ... 1<=x<y<=n .... x*y<=2n

A211267 ... 1<=x<y<=n .... x*y<=3n

A181972 ... 1<=x<y<=n .... x*y<=floor(n/2)

A038548 ... 1<=x<=y<=n ... x*y=n

A072670 ... 1<=x<=y<=n ... x*y=n+1

A211270 ... 1<=x<=y<=n ... x*y=2n

A211271 ... 1<=x<=y<=n ... x*y=3n

A211272 ... 1<=x<=y<=n ... x*y=floor(n/2)

A094820 ... 1<=x<=y<=n ... x*y<=n

A091627 ... 1<=x<=y<=n ... x*y<=n+1

A211273 ... 1<=x<=y<=n ... x*y<=2n

A211274 ... 1<=x<=y<=n ... x*y<=3n

A211275 ... 1<=x<=y<=n ... x*y<=floor(n/2)

Links

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

Example

a(6) counts these pairs: (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4).

Mathematica

a = 1; b = n; z1 = 120;
t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
{y, x + 1, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 1, z1}]           (* A056924 *)
Table[c[n, n + 1], {n, 1, z1}]       (* A211159 *)
Table[c[n, 2*n], {n, 1, z1}]         (* A211261 *)
Table[c[n, 3*n], {n, 1, z1}]         (* A211262 *)
Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211263 *)
Print
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Table[c1[n, n], {n, 1, z1}]          (* A211264 *)
Table[c1[n, n + 1], {n, 1, z1}]      (* A211265 *)
Table[c1[n, 2*n], {n, 1, z1}]        (* A211266 *)
Table[c1[n, 3*n], {n, 1, z1}]        (* A211267 *)
Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)

Crossrefs

Cf. A211261, A211264.

Sequence in context: A057640 A182136 A335408 * A378365 A037030 A277719

Adjacent sequences: A211263 A211264 A211265 * A211267 A211268 A211269

Keyword

nonn

Author

Clark Kimberling, Apr 06 2012

Status

approved