%I #7 Aug 12 2015 21:17:28
%S 1,1,2,2,0,2,2,2,0,3,4,0,0,0,2,2,4,2,0,0,4,6,0,0,0,0,0,2,4,4,0,3,0,0,
%T 0,4,6,0,4,0,0,0,0,0,3,4,8,0,0,2,0,0,0,0,4
%N Triangle T(n,k)= tau(k)*phi(n/k) if k|n, else T(n,k)=0.
%C Tau is the number of divisors A000005, and phi the Euler totient A000010.
%F T(n,k) = A000005(k)*A054523(n,k).
%F T(n,1) = A000010(n).
%F T(n,n) = A000005(n).
%F Sum_{k=1..n} T(n,k) = A000203(n).
%e First few rows of the triangle are:
%e 1;
%e 1, 2;
%e 2, 0, 2;
%e 2, 2, 0, 3;
%e 4, 0, 0, 0, 2;
%e 2, 4, 2, 0, 0, 4;
%e 6, 0, 0, 0, 0, 0, 2;
%e 4, 4, 0, 3, 0, 0, 0, 4;
%e ...
%p A127527 := proc(n,k) if n mod k = 0 then numtheory[tau](k)*numtheory[phi](n/k) ; else 0; end if; end proc: # _R. J. Mathar_, Apr 11 2011
%Y Cf. A054523, A000005, A000010, A000203.
%K nonn,tabl,easy
%O 1,3
%A _Gary W. Adamson_, Jan 17 2007
%E Definition clarified by _R. J. Mathar_, Apr 11 2011