A211261 Number of integer pairs (x,y) such that 0<x<y<=n and x*y=2n.

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

Offset

1,6

Comments

For a guide to related sequences, see A211266.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = floor(A000005(2*n)/2)-1. - Antti Karttunen, Sep 30 2018, after David A. Corneth's PARI-program

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 *)

Prog

(PARI) A211261(n) = sumdiv(2*n, y, (((2*n/y)<y)&&(y<=n))); \\ Antti Karttunen, Sep 30 2018
(PARI) a(n) = numdiv(n<<1)>>1-1 \\ David A. Corneth, Sep 30 2018

Crossrefs

Cf. A000005, A099777, A211266, A211270.

Sequence in context: A344234 A338912 A086598 * A344174 A336431 A074746

Adjacent sequences: A211258 A211259 A211260 * A211262 A211263 A211264

Keyword

nonn

Author

Clark Kimberling, Apr 06 2012

Status

approved