A100449 -id:A100449 - cp's OEIS frontend

A225529 Number of distinct products i*j over all pairs (i,j) with i,j >= 0 and i+j <= n and gcd(i,j) <= 1.

1, 1, 2, 3, 4, 6, 7, 9, 11, 14, 16, 20, 22, 26, 29, 32, 35, 41, 44, 50, 54, 59, 63, 70, 74, 80, 85, 92, 98, 108, 112, 121, 129, 137, 144, 153, 158, 170, 177, 186, 192, 204, 210, 222, 231, 240, 249, 262, 270, 284, 293, 305, 315, 331, 340, 353

Offset: 0

Robert Price, May 09 2013

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

Robert Price, Table of n, a(n) for n = 0..400

Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213208.

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

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

Original entry on oeis.org

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

Robert Price, Jun 03 2013

nonn

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

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

Cf. A064608, A100449.

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

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}]

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

cp's OEIS Frontend

A225529 Number of distinct products i*j over all pairs (i,j) with i,j >= 0 and i+j <= n and gcd(i,j) <= 1.

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