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 A127172 #13 Feb 15 2022 11:10:46 %S A127172 1,3,1,3,0,1,6,3,0,1,3,0,0,0,1,9,3,3,0,0,1,3,0,0,0,0,0,1,10,6,0,3,0,0, %T A127172 0,1,6,0,3,0,0,0,0,0,1,9,3,0,0,0,3,0,0,0,0,1 %N A127172 Cube of A051731. %C A127172 Nonzero terms in every column = A007425: (1, 3, 3, 6, 3, 9, 3, ...). %C A127172 Row sums = A007426: (1, 4, 4, 20, 4, 16, ...). %C A127172 A127172 * mu(n) = d(n); or A127172 * A008683 = A000005. %C A127172 A127172 * d(n) = tau_5(n); or A127172 * A000005 = A061200. %C A127172 A127172 * phi(n) = A007429: (1, 4, 5, 11, 7, 20, ...); or: A127172 * A000010 = A007429. %C A127172 Note that A051731 * d(n) = row sums of A127172; or A051731 * A000005 = A007425. %C A127172 Also, A126988 * mu(n) = phi(n); or A126988 * A008683 = A000010. %C A127172 A126988 * phi(n) = A018804: (1, 3, 5, 8, 9, 15, ...); = A127170 * mu(n). %F A127172 Cube of A051731 A007425: (1, 3, 3, 6, 3, 9, 3, ...) in every column k, interspersed with (k-1) zeros. %e A127172 First few rows of the triangle: %e A127172 1; %e A127172 3, 1; %e A127172 3, 0, 1; %e A127172 6, 3, 0, 1; %e A127172 3, 0, 0, 0, 1; %e A127172 9, 3, 3, 0, 0, 1; %e A127172 3, 0, 0, 0, 0, 0, 1; %e A127172 10, 6, 0, 3, 0, 0, 0, 1; %e A127172 6, 0, 3, 0, 0, 0, 0, 0, 1; %e A127172 9, 3, 0, 0, 3, 0, 0, 0, 0, 1; %e A127172 ... %Y A127172 Cf. A000005, A007425, A127170, A051731, A007429, A000010, A126988, A018804. %K A127172 nonn,tabl,uned %O A127172 1,2 %A A127172 _Gary W. Adamson_, Jan 06 2007