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A127528 Triangle T(n,k) read by rows: tau(n)*phi(n/k) if k|n, else 0.

%I A127528 #9 Aug 12 2015 21:21:28
%S A127528 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 A127528 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 A127528 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 A127528 Triangle T(n,k) read by rows: tau(n)*phi(n/k) if k|n, else 0.
%F A127528 T(n,k) = A000005(n) * A054523(n,k).
%F A127528 T(n,1) = A062355(n).
%F A127528 T(n,n) = A000005(n).
%F A127528 sum_{k=1..n} T(n,k) = A038040(n).
%e A127528 First few rows of the triangle are:
%e A127528 1;
%e A127528 2, 2;
%e A127528 4, 0, 2;
%e A127528 6, 3, 0, 3;
%e A127528 8, 0, 0, 0, 2;
%e A127528 8, 8, 4, 0, 0, 4;
%e A127528 12, 0, 0, 0, 0, 0, 2;
%e A127528 ...
%p A127528 A127528 := proc(n,k) if n mod k = 0 then numtheory[tau](n)*numtheory[phi](n/k) ; else  0; end if; end proc:
%p A127528 seq(seq(A127528(n,k),k=1..n),n=1..15) ; # _R. J. Mathar_, Feb 05 2011
%Y A127528 Cf. A054523, A127527, A062355, A038040, A000005.
%K A127528 nonn,tabl,easy
%O A127528 1,2
%A A127528 _Gary W. Adamson_, Jan 17 2007