cp's OEIS Frontend

A211267 Number of integer pairs (x,y) such that 0 and x*y<=3n.

%I A211267 #10 Oct 18 2019 16:46:36
%S A211267 0,1,3,6,9,12,16,20,23,28,32,37,40,46,51,56,60,65,71,77,81,87,91,99,
%T A211267 103,109,115,121,125,133,138,145,150,156,163,169,174,181,187,196,199,
%U A211267 207,212,220,226,232,239,247,252,259,265,274,277,287,293,301,307
%N A211267 Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=3n.
%C A211267 For a guide to related sequences, see A211266.
%H A211267 Robert Israel, <a href="/A211267/b211267.txt">Table of n, a(n) for n = 1..10000</a>
%e A211267 a(5) counts these pairs: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5).
%p A211267 N:= 100: # for a(1)..a(N)
%p A211267 L:= Vector(N):
%p A211267 for x from 1 to floor(sqrt(N)) do
%p A211267    for y from x+1 while y<=N and x*y<=3*N do
%p A211267      n0:= max(y, ceil(x*y/3));
%p A211267      L[n0]:= L[n0]+1;
%p A211267 od od:
%p A211267 ListTools:-PartialSums(convert(L,list)); # _Robert Israel_, Oct 18 2019
%t A211267 a = 1; b = n; z1 = 120;
%t A211267 t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t A211267 {y, x + 1, b}]]
%t A211267 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211267 Table[c[n, n], {n, 1, z1}]           (* A056924 *)
%t A211267 Table[c[n, n + 1], {n, 1, z1}]       (* A211159 *)
%t A211267 Table[c[n, 2*n], {n, 1, z1}]         (* A211261 *)
%t A211267 Table[c[n, 3*n], {n, 1, z1}]         (* A211262 *)
%t A211267 Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211263 *)
%t A211267 Print
%t A211267 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211267 Table[c1[n, n], {n, 1, z1}]          (* A211264 *)
%t A211267 Table[c1[n, n + 1], {n, 1, z1}]      (* A211265 *)
%t A211267 Table[c1[n, 2*n], {n, 1, z1}]        (* A211266 *)
%t A211267 Table[c1[n, 3*n], {n, 1, z1}]        (* A211267 *)
%t A211267 Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)
%Y A211267 Cf. A211266.
%K A211267 nonn
%O A211267 1,3
%A A211267 _Clark Kimberling_, Apr 06 2012