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A211273 Number of integer pairs (x,y) such that 0 and x*y<=2n.

%I A211273 #9 Jan 22 2025 20:06:07
%S A211273 1,3,5,7,10,13,15,19,22,25,28,32,35,39,43,46,49,55,57,62,66,69,73,78,
%T A211273 82,86,90,95,98,104,106,112,117,120,125,131,133,138,143,148,152,158,
%U A211273 161,166,172,176,179,186,189,196,200,204,209,215,219,225,229,233
%N A211273 Number of integer pairs (x,y) such that 0<x<=y<=n and x*y<=2n.
%C A211273 For a guide to related sequences, see A211266.
%e A211273 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 A211273 a = 1; b = n; z1 = 120;
%t A211273 t[n_] :=  t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t A211273 {y, x, b}]]
%t A211273 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211273 Table[c[n, n], {n, 1, z1}]           (* A038548 *)
%t A211273 Table[c[n, n + 1], {n, 1, z1}]       (* A072670 *)
%t A211273 Table[c[n, 2*n], {n, 1, z1}]         (* A211270 *)
%t A211273 Table[c[n, 3*n], {n, 1, z1}]         (* A211271 *)
%t A211273 Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211272 *)
%t A211273 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211273 Print
%t A211273 Table[c1[n, n], {n, 1, z1}]          (* A094820 *)
%t A211273 Table[c1[n, n + 1], {n, 1, z1}]      (* A091627 *)
%t A211273 Table[c1[n, 2*n], {n, 1, z1}]        (* A211273 *)
%t A211273 Table[c1[n, 3*n], {n, 1, z1}]        (* A211274 *)
%t A211273 Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)
%Y A211273 Cf. A211266.
%K A211273 nonn
%O A211273 1,2
%A A211273 _Clark Kimberling_, Apr 07 2012
%E A211273 a(1)-a(2) corrected by _Sean A. Irvine_, Jan 22 2025