This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226357 #26 Aug 02 2019 03:24:49 %S A226357 1,27,75,147,243,363,483,651,819,1011,1179,1443,1683,1995,2211,2475, %T A226357 2763,3171,3459,3915,4251,4611,4923,5475,5883,6411,6771,7275,7707, %U A226357 8403,8811,9555,10059,10611,11067,11715,12291,13179,13683,14331,14931,15915,16419 %N A226357 Number of ordered triples (i,j,k) with |i|,|j|,|k|,|i*j*k| <= n and gcd(i,j,k) <= 1. %C A226357 Note that gcd(0,m) = m for any m. %H A226357 Robert Price, <a href="/A226357/b226357.txt">Table of n, a(n) for n = 0..100</a> %t A226357 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 A226357 |i| + |j| + |k| <= n instead of |i*j*k| <= n: A100450. %Y A226357 This sequence (A226357) without the GCD qualifier: A226359. %Y A226357 Distinct sums i+j+k with the GCD qualifier: A222947. %Y A226357 Distinct sums i+j+k without the GCD qualifier: A222945. %Y A226357 Distinct products i*j*k with or without the GCD qualifier is 2n+1: A005408. %Y A226357 With the further restriction i,j,k >= 0 ... %Y A226357 Distinct sums i+j+k <= n with the GCD qualifier: A223133. %Y A226357 Distinct sums i+j+k <= n without the GCD qualifier: A223134. %Y A226357 Distinct products i*j*k with or without the GCD qualifier is n+1: A000217(n+1). %Y A226357 Distinct sums i+j+k with i*j*k = n with the GCD qualifier: A223135. %Y A226357 Distinct sums i+j+k with i*j*k = n without the GCD qualifier: A226378. %Y A226357 Distinct products i*j*k with i*j*k = n with or without the GCD qualifier is trivial and always 1: A000012. %Y A226357 Ordered triples with the product <= n with the GCD qualifier: A226001. %Y A226357 Ordered triples with the product <= n without the GCD qualifier: A226600. %Y A226357 Ordered triples with the product = n with the GCD qualifier: A226602. %Y A226357 Ordered triples with the product = n without the GCD qualifier: A007425. %K A226357 nonn %O A226357 0,2 %A A226357 _Robert Price_, Jun 04 2013