A226323 Number of ordered pairs (i,j) with |i| * |j| <= n and gcd(i,j) <= 1.

1, 9, 17, 25, 33, 41, 57, 65, 73, 81, 97, 105, 121, 129, 145, 161, 169, 177, 193, 201, 217, 233, 249, 257, 273, 281, 297, 305, 321, 329, 361, 369, 377, 393, 409, 425, 441, 449, 465, 481, 497, 505, 537, 545, 561, 577, 593, 601, 617, 625, 641, 657, 673, 681, 697

Offset: 0

Author

Robert Price, Jun 03 2013

Keywords

• nonn

Comments

Note that gcd(0,m) = m for any m.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A064608, A100449.

Programs

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, 5+4*add(mobius(k)^2*floor(n/k), k=1..n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Jun 03 2013

Mathematica

f[n_] := Length[Complement[Union[Flatten[Table[If[Abs[i]*Abs[j] ≤ n && GCD[i, j] ≤ 1, {i, j}], {i, -n, n}, {j, -n, n}], 1]], {Null}]]; Table[f[n], {n, 0, 100}]

Formula

a(n) = 4*A064608(n) + 5 for n > 0, a(0)=1. - Alois P. Heinz, Jun 03 2013