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A127465 Triangle read by rows: T(n,k) = k*phi(n/k) if k|n, T(n,k)=0 otherwise.

%I A127465 #10 Mar 21 2016 03:15:24
%S A127465 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 A127465 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 A127465 4,6,8,0,6,0,0,0,0,0,12
%N A127465 Triangle read by rows: T(n,k) = k*phi(n/k) if k|n, T(n,k)=0 otherwise.
%H A127465 Robert Israel, <a href="/A127465/b127465.txt">Table of n, a(n) for n = 1..10011</a> (rows 1 to 141, flattened)
%F A127465 T(n,k) = k*A054523(n,k).
%e A127465 First few rows of the triangle are:
%e A127465 1;
%e A127465 1, 2;
%e A127465 2, 0, 3;
%e A127465 2, 2, 0, 4;
%e A127465 4, 0, 0, 0, 5;
%e A127465 2, 4, 3, 0, 0, 6;
%e A127465 6, 0, 0, 0, 0, 0, 7;
%e A127465 4, 4, 0, 4, 0, 0, 0, 8;
%e A127465 ...
%p A127465 A127465 := proc(n,k)
%p A127465         if n mod k = 0 then
%p A127465                 k*numtheory[phi](n/k) ;
%p A127465         else
%p A127465                 0;
%p A127465         end if;
%p A127465 end proc:
%p A127465 seq(seq(A127465(n,m),m=1..n),n=1..12) ; # _R. J. Mathar_, Nov 08 2011
%Y A127465 Cf. A054523, A000010 (column k=1), A018804 (row sums).
%K A127465 nonn,tabl,easy
%O A127465 1,3
%A A127465 _Gary W. Adamson_, Jan 15 2007