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A211271 Number of integer pairs (x,y) such that 0 and x*y=3n.

%I A211271 #10 Jan 15 2025 22:45:39
%S A211271 0,0,1,1,1,1,1,2,1,2,1,3,1,2,2,3,1,2,1,4,2,2,1,4,2,2,2,4,1,4,1,4,2,2,
%T A211271 3,4,1,2,2,6,1,4,1,4,3,2,1,6,2,4,2,4,1,3,3,6,2,2,1,7,1,2,3,5,3,4,1,4,
%U A211271 2,6,1,6,1,2,4,4,3,4,1,8,2,2,1,7,3,2,2,6,1,6,3,4,2,2,3,7,1,4,3,7,1,4,1,6,5,2,1,6
%N A211271 Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=3n.
%C A211271 For a guide to related sequences, see A211266.
%H A211271 Antti Karttunen, <a href="/A211271/b211271.txt">Table of n, a(n) for n = 1..20000</a>
%e A211271 a(3) counts this pair: (3,3). - _Antti Karttunen_, Jan 15 2025
%e A211271 a(20) counts these pairs: (3,20), (4,15), (5,12), (6,10).
%t A211271 a = 1; b = n; z1 = 120;
%t A211271 t[n_] :=  t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t A211271  {y, x, b}]]
%t A211271 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211271 Table[c[n, n], {n, 1, z1}]           (* A038548 *)
%t A211271 Table[c[n, n + 1], {n, 1, z1}]       (* A072670 *)
%t A211271 Table[c[n, 2*n], {n, 1, z1}]         (* A211270 *)
%t A211271 Table[c[n, 3*n], {n, 1, z1}]         (* A211271 *)
%t A211271 Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211272 *)
%t A211271 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211271 Print
%t A211271 Table[c1[n, n], {n, 1, z1}]          (* A094820 *)
%t A211271 Table[c1[n, n + 1], {n, 1, z1}]      (* A091627 *)
%t A211271 Table[c1[n, 2*n], {n, 1, z1}]        (* A211273 *)
%t A211271 Table[c1[n, 3*n], {n, 1, z1}]        (* A211274 *)
%t A211271 Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)
%o A211271 (PARI) A211271(n) = { my(n3=3*n); sumdiv(n3,d,(d <= (n3/d) && (n3/d) <= n)); }; \\ _Antti Karttunen_, Jan 15 2025
%Y A211271 Cf. A211266.
%Y A211271 Cf. also A211262.
%K A211271 nonn
%O A211271 1,8
%A A211271 _Clark Kimberling_, Apr 07 2012
%E A211271 Data section extended up to a(108) and a(3) corrected from 0 to 1 by _Antti Karttunen_, Jan 15 2025