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A127481 Triangle T(n,k) read by rows: T(n,k) = sum_{l=k..n, l|n, k|l} l*phi(k).

%I A127481 #9 Sep 06 2013 16:43:57
%S A127481 1,3,2,4,0,6,7,6,0,8,6,0,0,0,20,12,8,18,0,0,12,8,0,0,0,0,0,42,15,14,0,
%T A127481 24,0,0,0,32,13,0,24,0,0,0,0,0,54,18,12,0,0,60,0,0,0,0,40,12,0,0,0,0,
%U A127481 0,0,0,0,0,110,28,24,42,32,0,36,0,0,0,0,0,48,14,0,0,0,0,0,0,0,0
%N A127481 Triangle T(n,k) read by rows: T(n,k) = sum_{l=k..n, l|n, k|l} l*phi(k).
%F A127481 T(n,1) = A000203(n).
%F A127481 T(n,n) = A002618(n).
%F A127481 T(n,k) =sum_{l=k..n} A127093(n,l) * A054522(l,k), the matrix product of the infinite lower triangular matrices.
%e A127481 First few rows of the triangle are:
%e A127481 1;
%e A127481 3, 2;
%e A127481 4, 0, 6;
%e A127481 7, 6, 0, 8;
%e A127481 6, 0, 0, 0, 20,
%e A127481 12, 8, 18, 0, 0, 12;
%e A127481 8, 0, 0, 0, 0, 0, 42;
%e A127481 15, 14, 0, 24, 0, 0, 0, 32;
%e A127481 ...
%p A127481 A127481 := proc(n,k)
%p A127481     a :=0 ;
%p A127481     for l from k to n do
%p A127481         if modp(n,l) =0 and modp(l,k) =0 then
%p A127481             a := a+l*numtheory[phi](k) ;
%p A127481         end if;
%p A127481     end do:
%p A127481     a ;
%p A127481 end proc: # _R. J. Mathar_, Sep 06 2013
%Y A127481 Cf. A054522, A127093, A001157 (row sums), A002618, A127466.
%K A127481 nonn,tabl,easy
%O A127481 1,2
%A A127481 _Gary W. Adamson_, Jan 15 2007