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A211274 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= 3n.

%I A211274 #9 Jan 22 2025 20:06:13
%S A211274 1,3,6,9,12,16,20,24,28,33,37,43,46,52,57,62,67,72,78,84,88,95,99,107,
%T A211274 111,117,124,130,134,142,147,154,159,166,173,179,184,191,197,206,210,
%U A211274 218,223,231,237,243,250,259,264,271,277,286,289,299,305,313
%N A211274 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= 3n.
%C A211274 For a guide to related sequences, see A211266.
%e A211274 a(4) counts these pairs: (1,1), (1,2), (1,3), (1,4), (2,3), (2,4), (3,3,), (3,4), (4,4).
%t A211274 a = 1; b = n; z1 = 120;
%t A211274 t[n_] :=  t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t A211274 {y, x, b}]]
%t A211274 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211274 Table[c[n, n], {n, 1, z1}]           (* A038548 *)
%t A211274 Table[c[n, n + 1], {n, 1, z1}]       (* A072670 *)
%t A211274 Table[c[n, 2*n], {n, 1, z1}]         (* A211270 *)
%t A211274 Table[c[n, 3*n], {n, 1, z1}]         (* A211271 *)
%t A211274 Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211272 *)
%t A211274 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211274 Print
%t A211274 Table[c1[n, n], {n, 1, z1}]          (* A094820 *)
%t A211274 Table[c1[n, n + 1], {n, 1, z1}]      (* A091627 *)
%t A211274 Table[c1[n, 2*n], {n, 1, z1}]        (* A211273 *)
%t A211274 Table[c1[n, 3*n], {n, 1, z1}]        (* A211274 *)
%t A211274 Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)
%Y A211274 Cf. A211266.
%K A211274 nonn
%O A211274 1,2
%A A211274 _Clark Kimberling_, Apr 07 2012
%E A211274 a(1)-a(3) corrected by _Sean A. Irvine_, Jan 22 2025