A211274 - OEIS

%I #9 Jan 22 2025 20:06:13

%S 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 111,117,124,130,134,142,147,154,159,166,173,179,184,191,197,206,210,

%U 218,223,231,237,243,250,259,264,271,277,286,289,299,305,313

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

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

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

%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

%E a(1)-a(3) corrected by _Sean A. Irvine_, Jan 22 2025