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

%I A211261 #17 Sep 30 2018 10:42:02
%S A211261 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,
%T A211261 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,
%U A211261 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
%N A211261 Number of integer pairs (x,y) such that 0<x<y<=n and x*y=2n.
%C A211261 For a guide to related sequences, see A211266.
%H A211261 Antti Karttunen, <a href="/A211261/b211261.txt">Table of n, a(n) for n = 1..65537</a>
%F A211261 a(n) = floor(A000005(2*n)/2)-1. - _Antti Karttunen_, Sep 30 2018, after _David A. Corneth_'s PARI-program
%t A211261 a = 1; b = n; z1 = 120;
%t A211261 t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t A211261 {y, x + 1, b}]]
%t A211261 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211261 Table[c[n, n], {n, 1, z1}]           (* A056924 *)
%t A211261 Table[c[n, n + 1], {n, 1, z1}]       (* A211159 *)
%t A211261 Table[c[n, 2*n], {n, 1, z1}]         (* A211261 *)
%t A211261 Table[c[n, 3*n], {n, 1, z1}]         (* A211262 *)
%t A211261 Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211263 *)
%t A211261 Print
%t A211261 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211261 Table[c1[n, n], {n, 1, z1}]          (* A211264 *)
%t A211261 Table[c1[n, n + 1], {n, 1, z1}]      (* A211265 *)
%t A211261 Table[c1[n, 2*n], {n, 1, z1}]        (* A211266 *)
%t A211261 Table[c1[n, 3*n], {n, 1, z1}]        (* A211267 *)
%t A211261 Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)
%o A211261 (PARI) A211261(n) = sumdiv(2*n,y,(((2*n/y)<y)&&(y<=n))); \\ _Antti Karttunen_, Sep 30 2018
%o A211261 (PARI) a(n) = numdiv(n<<1)>>1-1 \\ _David A. Corneth_, Sep 30 2018
%Y A211261 Cf. A000005, A099777, A211266, A211270.
%K A211261 nonn
%O A211261 1,6
%A A211261 _Clark Kimberling_, Apr 06 2012