A127465 - OEIS

%I #10 Mar 21 2016 03:15:24

%S 1,1,2,2,0,3,2,2,0,4,4,0,0,0,5,2,4,3,0,0,6,6,0,0,0,0,0,7,4,4,0,4,0,0,

%T 0,8,6,0,6,0,0,0,0,0,9,4,8,0,0,5,0,0,0,0,10,10,0,0,0,0,0,0,0,0,0,11,4,

%U 4,6,8,0,6,0,0,0,0,0,12

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

%H Robert Israel, <a href="/A127465/b127465.txt">Table of n, a(n) for n = 1..10011</a> (rows 1 to 141, flattened)

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

%e First few rows of the triangle are:

%e 1;

%e 1, 2;

%e 2, 0, 3;

%e 2, 2, 0, 4;

%e 4, 0, 0, 0, 5;

%e 2, 4, 3, 0, 0, 6;

%e 6, 0, 0, 0, 0, 0, 7;

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

%e ...

%p A127465 := proc(n,k)

%p         if n mod k = 0 then

%p                 k*numtheory[phi](n/k) ;

%p         else

%p                 0;

%p         end if;

%p end proc:

%p seq(seq(A127465(n,m),m=1..n),n=1..12) ; # _R. J. Mathar_, Nov 08 2011

%Y Cf. A054523, A000010 (column k=1), A018804 (row sums).

%K nonn,tabl,easy

%O 1,3

%A _Gary W. Adamson_, Jan 15 2007