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Triangle T(n,k) read by rows: tau(n)*phi(n/k) if k|n, else 0.
2

%I #9 Aug 12 2015 21:21:28

%S 1,2,2,4,0,2,6,3,0,3,8,0,0,0,2,8,8,4,0,0,4,12,0,0,0,0,0,2,16,8,0,4,0,

%T 0,0,4,18,0,6,0,0,0,0,0,3,16,16,0,0,4,0,0,0,0,4,20,0,0,0,0,0,0,0,0,0,

%U 2,24,12,12,12,0,6,0,0,0,0,0,6,24,0,0,0,0,0,0,0,0,0,0,0,2,24,24

%N Triangle T(n,k) read by rows: tau(n)*phi(n/k) if k|n, else 0.

%F T(n,k) = A000005(n) * A054523(n,k).

%F T(n,1) = A062355(n).

%F T(n,n) = A000005(n).

%F sum_{k=1..n} T(n,k) = A038040(n).

%e First few rows of the triangle are:

%e 1;

%e 2, 2;

%e 4, 0, 2;

%e 6, 3, 0, 3;

%e 8, 0, 0, 0, 2;

%e 8, 8, 4, 0, 0, 4;

%e 12, 0, 0, 0, 0, 0, 2;

%e ...

%p A127528 := proc(n,k) if n mod k = 0 then numtheory[tau](n)*numtheory[phi](n/k) ; else 0; end if; end proc:

%p seq(seq(A127528(n,k),k=1..n),n=1..15) ; # _R. J. Mathar_, Feb 05 2011

%Y Cf. A054523, A127527, A062355, A038040, A000005.

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Jan 17 2007