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A211262 Number of integer pairs (x,y) such that 0 and x*y=3n.

%I A211262 #9 Jan 15 2025 22:45:36
%S A211262 0,0,0,1,1,1,1,2,1,2,1,2,1,2,2,3,1,2,1,4,2,2,1,4,2,2,1,4,1,4,1,4,2,2,
%T A211262 3,4,1,2,2,6,1,4,1,4,3,2,1,5,2,4,2,4,1,3,3,6,2,2,1,7,1,2,3,5,3,4,1,4,
%U A211262 2,6,1,6,1,2,3,4,3,4,1,8,2,2,1,7,3,2,2,6,1,6,3,4,2,2,3,7,1,4,3,7,1,4,1,6,5,2,1,5
%N A211262 Number of integer pairs (x,y) such that 0<x<y<=n and x*y=3n.
%C A211262 For a guide to related sequences, see A211266.
%H A211262 Antti Karttunen, <a href="/A211262/b211262.txt">Table of n, a(n) for n = 1..20000</a>
%t A211262 a = 1; b = n; z1 = 120;
%t A211262 t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t A211262  {y, x + 1, b}]]
%t A211262 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211262 Table[c[n, n], {n, 1, z1}]           (* A056924 *)
%t A211262 Table[c[n, n + 1], {n, 1, z1}]       (* A211159 *)
%t A211262 Table[c[n, 2*n], {n, 1, z1}]         (* A211261 *)
%t A211262 Table[c[n, 3*n], {n, 1, z1}]         (* A211262 *)
%t A211262 Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211263 *)
%t A211262 Print
%t A211262 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211262 Table[c1[n, n], {n, 1, z1}]          (* A211264 *)
%t A211262 Table[c1[n, n + 1], {n, 1, z1}]      (* A211265 *)
%t A211262 Table[c1[n, 2*n], {n, 1, z1}]        (* A211266 *)
%t A211262 Table[c1[n, 3*n], {n, 1, z1}]        (* A211267 *)
%t A211262 Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)
%o A211262 (PARI) A211262(n) = { my(n3=3*n); sumdiv(n3,d,(d < (n3/d) && (n3/d) <= n)); }; \\ _Antti Karttunen_, Jan 15 2025
%Y A211262 Cf. A211266
%Y A211262 Cf. also A211271.
%K A211262 nonn
%O A211262 1,8
%A A211262 _Clark Kimberling_, Apr 06 2012
%E A211262 Data section extended up to a(108) by _Antti Karttunen_, Jan 15 2025