A211272 Number of integer pairs (x,y) such that 0

0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 2, 2, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 2, 2, 2, 2, 1, 1, 4, 4, 2, 2, 2, 2, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 3, 3, 2, 2, 2, 2, 2, 2, 5, 5, 1, 1, 2, 2, 2, 2, 4, 4, 1, 1, 4, 4, 1, 1, 3, 3, 3, 3, 2, 2, 1, 1, 5, 5, 2, 2

Offset: 1

Author

Clark Kimberling, Apr 07 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211266.

Examples

			a(24) counts these pairs: (1,12), (2,6), (3,4).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A211266.

Programs

Magma

[0] cat [Ceiling(#Divisors( Floor(n/2))/2):n in [2..100]]; // Marius A. Burtea, Feb 07 2020

Maple

[seq(ceil(numtheory:-tau(floor(n/2))/2),n=1..100)]; - Robert Israel, Feb 07 2020

Mathematica

a = 1; b = n; z1 = 120;
t[n_] :=  t[n] = Flatten[Table[x*y, {x, a, b - 1},
{y, x, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 1, z1}]           (* A038548 *)
Table[c[n, n + 1], {n, 1, z1}]       (* A072670 *)
Table[c[n, 2*n], {n, 1, z1}]         (* A211270 *)
Table[c[n, 3*n], {n, 1, z1}]         (* A211271 *)
Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211272 *)
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Print
Table[c1[n, n], {n, 1, z1}]          (* A094820 *)
Table[c1[n, n + 1], {n, 1, z1}]      (* A091627 *)
Table[c1[n, 2*n], {n, 1, z1}]        (* A211273 *)
Table[c1[n, 3*n], {n, 1, z1}]        (* A211274 *)
Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)

Formula

a(n) = ceiling(A000005(floor(n/2))/2). - Robert Israel, Feb 07 2020