A226357 Number of ordered triples (i,j,k) with |i|,|j|,|k|,|i*j*k| <= n and gcd(i,j,k) <= 1.

1, 27, 75, 147, 243, 363, 483, 651, 819, 1011, 1179, 1443, 1683, 1995, 2211, 2475, 2763, 3171, 3459, 3915, 4251, 4611, 4923, 5475, 5883, 6411, 6771, 7275, 7707, 8403, 8811, 9555, 10059, 10611, 11067, 11715, 12291, 13179, 13683, 14331, 14931, 15915, 16419

Offset: 0

Author

Robert Price, Jun 04 2013

Keywords

• nonn

Comments

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

Links

• Robert Price, Table of n, a(n) for n = 0..100

Crossrefs

|i| + |j| + |k| <= n instead of |i*j*k| <= n: A100450.

This sequence (A226357) without the GCD qualifier: A226359.

Distinct sums i+j+k with the GCD qualifier: A222947.

Distinct sums i+j+k without the GCD qualifier: A222945.

Distinct products i*j*k with or without the GCD qualifier is 2n+1: A005408.

With the further restriction i,j,k >= 0 ...

Distinct sums i+j+k <= n with the GCD qualifier: A223133.

Distinct sums i+j+k <= n without the GCD qualifier: A223134.

Distinct products i*j*k with or without the GCD qualifier is n+1: A000217(n+1).

Distinct sums i+j+k with i*j*k = n with the GCD qualifier: A223135.

Distinct sums i+j+k with i*j*k = n without the GCD qualifier: A226378.

Distinct products i*j*k with i*j*k = n with or without the GCD qualifier is trivial and always 1: A000012.

Ordered triples with the product <= n with the GCD qualifier: A226001.

Ordered triples with the product <= n without the GCD qualifier: A226600.

Ordered triples with the product = n with the GCD qualifier: A226602.

Ordered triples with the product = n without the GCD qualifier: A007425.

Programs

Mathematica

f[n_] := Length[Complement[Union[Flatten[Table[If[Abs[i*j*k] <=  n && GCD[i, j, k] <= 1, {i, j, k}], {i, -n, n}, {j, -n, n}, {k, -n, n}], 2]], {Null}]]; Table[f[n], {n, 0, 100}]