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Number of integer pairs (x,y) such that 0<x<=y<=n and x*y<=2n.
7

%I #6 Apr 14 2012 00:55:30

%S 0,2,5,7,10,13,15,19,22,25,28,32,35,39,43,46,49,55,57,62,66,69,73,78,

%T 82,86,90,95,98,104,106,112,117,120,125,131,133,138,143,148,152,158,

%U 161,166,172,176,179,186,189,196,200,204,209,215,219,225,229,233

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

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

%e a(5) counts these pairs: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3)

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

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

%t {y, x, b}]]

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

%t Table[c[n, n], {n, 1, z1}] (* A038548 *)

%t Table[c[n, n + 1], {n, 1, z1}] (* A072670 *)

%t Table[c[n, 2*n], {n, 1, z1}] (* A211270 *)

%t Table[c[n, 3*n], {n, 1, z1}] (* A211271 *)

%t Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211272 *)

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

%t Print

%t Table[c1[n, n], {n, 1, z1}] (* A094820 *)

%t Table[c1[n, n + 1], {n, 1, z1}] (* A091627 *)

%t Table[c1[n, 2*n], {n, 1, z1}] (* A211273 *)

%t Table[c1[n, 3*n], {n, 1, z1}] (* A211274 *)

%t Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)

%Y Cf. A211266.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 07 2012