A127481 - OEIS

%I #9 Sep 06 2013 16:43:57

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

%F T(n,1) = A000203(n).

%F T(n,n) = A002618(n).

%F T(n,k) =sum_{l=k..n} A127093(n,l) * A054522(l,k), the matrix product of the infinite lower triangular matrices.

%e First few rows of the triangle are:

%e 1;

%e 3, 2;

%e 4, 0, 6;

%e 7, 6, 0, 8;

%e 6, 0, 0, 0, 20,

%e 12, 8, 18, 0, 0, 12;

%e 8, 0, 0, 0, 0, 0, 42;

%e 15, 14, 0, 24, 0, 0, 0, 32;

%e ...

%p A127481 := proc(n,k)

%p     a :=0 ;

%p     for l from k to n do

%p         if modp(n,l) =0 and modp(l,k) =0 then

%p             a := a+l*numtheory[phi](k) ;

%p         end if;

%p     end do:

%p     a ;

%p end proc: # _R. J. Mathar_, Sep 06 2013

%Y Cf. A054522, A127093, A001157 (row sums), A002618, A127466.

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Jan 15 2007