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