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A226357
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Number of ordered triples (i,j,k) with |i|,|j|,|k|,|i*j*k| <= n and gcd(i,j,k) <= 1.
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11
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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
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OFFSET
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0,2
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COMMENTS
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Note that gcd(0,m) = m for any m.
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LINKS
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MATHEMATICA
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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}]
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CROSSREFS
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|i| + |j| + |k| <= n instead of |i*j*k| <= n: A100450.
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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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