A211271 Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=3n.

0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 4, 2, 2, 1, 4, 2, 2, 2, 4, 1, 4, 1, 4, 2, 2, 3, 4, 1, 2, 2, 6, 1, 4, 1, 4, 3, 2, 1, 6, 2, 4, 2, 4, 1, 3, 3, 6, 2, 2, 1, 7, 1, 2, 3, 5, 3, 4, 1, 4, 2, 6, 1, 6, 1, 2, 4, 4, 3, 4, 1, 8, 2, 2, 1, 7, 3, 2, 2, 6, 1, 6, 3, 4, 2, 2, 3, 7, 1, 4, 3, 7, 1, 4, 1, 6, 5, 2, 1, 6

Offset

1,8

Comments

For a guide to related sequences, see A211266.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Example

a(3) counts this pair: (3,3). - Antti Karttunen, Jan 15 2025
a(20) counts these pairs: (3,20), (4,15), (5,12), (6,10).

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 *)

Prog

(PARI) A211271(n) = { my(n3=3*n); sumdiv(n3, d, (d <= (n3/d) && (n3/d) <= n)); }; \\ Antti Karttunen, Jan 15 2025

Crossrefs

Cf. A211266.

Cf. also A211262.

Sequence in context: A178691 A329313 A329312 * A124768 A321014 A072527

Adjacent sequences: A211268 A211269 A211270 * A211272 A211273 A211274

Keyword

nonn,changed

Author

Clark Kimberling, Apr 07 2012

Extensions

Data section extended up to a(108) and a(3) corrected from 0 to 1 by Antti Karttunen, Jan 15 2025

Status

approved