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%I #9 Feb 18 2022 22:47:01
%S 1,2,1,2,0,1,4,2,0,1,4,0,0,0,1,4,2,2,0,0,1,6,0,0,0,0,0,1,8,4,0,2,0,0,
%T 0,1,6,0,2,0,0,0,0,0,1,8,4,0,0,2,0,0,0,0,1,10,0,0,0,0,0,0,0,0,0,1,8,4,
%U 4,2,0,2,0,0,0,0,0,1,12,0,0,0,0,0,0,0,0,0,0,0,1
%N A054523 * A115361.
%C row sums = A129527: (1, 3, 3, 7, 5, 9, 7, 15, ...). Left column = phi(2*n), A062570: (1, 2, 2, 4, 4, 4, 6, 8, ...).
%H Andrew Howroyd, <a href="/A129559/b129559.txt">Table of n, a(n) for n = 1..1275</a>
%F Equals A054523 * A115361 as infinite lower triangular matrices.
%F T(n,k) = phi(2*n/k) for k | n, T(n,k) = 0 otherwise. - _Andrew Howroyd_, Aug 07 2018
%e First few rows of the triangle:
%e 1;
%e 2, 1;
%e 2, 0, 1;
%e 4, 2, 0, 1;
%e 4, 0, 0, 0, 1;
%e 4, 2, 2, 0, 0, 1;
%e 6, 0, 0, 0, 0, 0, 1;
%e 8, 4, 0, 2, 0, 0, 0, 1;
%e ...
%o (PARI) T(n, k)=if(n%k, 0, eulerphi(2*n/k)) \\ _Andrew Howroyd_, Aug 07 2018
%Y Column 1 is A062570.
%Y Row sums are A129527 (inverse Moebius transform of A062570).
%Y Cf. A054523, A115361.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Apr 20 2007
%E Terms a(56) and beyond from _Andrew Howroyd_, Aug 07 2018