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%I #26 Aug 02 2019 03:24:49
%S 1,27,75,147,243,363,483,651,819,1011,1179,1443,1683,1995,2211,2475,
%T 2763,3171,3459,3915,4251,4611,4923,5475,5883,6411,6771,7275,7707,
%U 8403,8811,9555,10059,10611,11067,11715,12291,13179,13683,14331,14931,15915,16419
%N Number of ordered triples (i,j,k) with |i|,|j|,|k|,|i*j*k| <= n and gcd(i,j,k) <= 1.
%C Note that gcd(0,m) = m for any m.
%H Robert Price, <a href="/A226357/b226357.txt">Table of n, a(n) for n = 0..100</a>
%t 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}]
%Y |i| + |j| + |k| <= n instead of |i*j*k| <= n: A100450.
%Y This sequence (A226357) without the GCD qualifier: A226359.
%Y Distinct sums i+j+k with the GCD qualifier: A222947.
%Y Distinct sums i+j+k without the GCD qualifier: A222945.
%Y Distinct products i*j*k with or without the GCD qualifier is 2n+1: A005408.
%Y With the further restriction i,j,k >= 0 ...
%Y Distinct sums i+j+k <= n with the GCD qualifier: A223133.
%Y Distinct sums i+j+k <= n without the GCD qualifier: A223134.
%Y Distinct products i*j*k with or without the GCD qualifier is n+1: A000217(n+1).
%Y Distinct sums i+j+k with i*j*k = n with the GCD qualifier: A223135.
%Y Distinct sums i+j+k with i*j*k = n without the GCD qualifier: A226378.
%Y Distinct products i*j*k with i*j*k = n with or without the GCD qualifier is trivial and always 1: A000012.
%Y Ordered triples with the product <= n with the GCD qualifier: A226001.
%Y Ordered triples with the product <= n without the GCD qualifier: A226600.
%Y Ordered triples with the product = n with the GCD qualifier: A226602.
%Y Ordered triples with the product = n without the GCD qualifier: A007425.
%K nonn
%O 0,2
%A _Robert Price_, Jun 04 2013
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