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Number of integer pairs (x,y) such that 0<x<y<=n and x*y=floor(n/2).
9

%I #4 Apr 11 2012 18:49:18

%S 0,0,0,1,1,1,1,1,1,1,1,2,2,1,1,2,2,1,1,2,2,1,1,3,3,1,1,2,2,2,2,2,2,1,

%T 1,3,3,1,1,3,3,2,2,2,2,1,1,4,4,1,1,2,2,2,2,3,3,1,1,4,4,1,1,3,3,2,2,2,

%U 2,2,2,4,4,1,1,2,2,2,2,4,4,1,1,4,4,1,1,3,3,3,3,2,2,1,1,5,5,1,1

%N Number of integer pairs (x,y) such that 0<x<y<=n and x*y=floor(n/2).

%C For a guide to related sequences, see A211266.

%e a(12) counts these pairs: (1,6) and (2,3).

%t a = 1; b = n; z1 = 120;

%t t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},

%t {y, x + 1, b}]]

%t c[n_, k_] := c[n, k] = Count[t[n], k]

%t Table[c[n, n], {n, 1, z1}] (* A056924 *)

%t Table[c[n, n + 1], {n, 1, z1}] (* A211159 *)

%t Table[c[n, 2*n], {n, 1, z1}] (* A211261 *)

%t Table[c[n, 3*n], {n, 1, z1}] (* A211262 *)

%t Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211263 *)

%t Print

%t c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]

%t Table[c1[n, n], {n, 1, z1}] (* A211264 *)

%t Table[c1[n, n + 1], {n, 1, z1}] (* A211265 *)

%t Table[c1[n, 2*n], {n, 1, z1}] (* A211266 *)

%t Table[c1[n, 3*n], {n, 1, z1}] (* A211267 *)

%t Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)

%Y Cf. A211266.

%K nonn

%O 1,12

%A _Clark Kimberling_, Apr 06 2012