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A127649 A127648 * A054523 as infinite lower triangular matrices.

%I A127649 #9 Oct 08 2023 09:01:51
%S A127649 1,2,2,6,0,3,8,4,0,4,20,0,0,0,5,12,12,6,0,0,6,42,0,0,0,0,0,7,32,16,0,
%T A127649 8,0,0,0,8,54,0,18,0,0,0,0,0,9,40,40,0,0,10,0,0,0,0,10,110,0,0,0,0,0,
%U A127649 0,0,0,0,11,48,24,24,24,0,12,0,0,0,0,0,12,156,0,0,0,0,0,0,0,0,0,0,0,13,84
%N A127649 A127648 * A054523 as infinite lower triangular matrices.
%C A127649 Natural number transform of A054523.
%C A127649 Row sums = n^2, left column = A002618
%F A127649 T(n,k)=n*A054523(n,k). - _R. J. Mathar_, Nov 01 2007
%F A127649 T(n,k) = Sum_{y=1..n} Sum_{x=1..n} [GCD(f(x,y), n) = k], where f(x,y) = x - y. - _Mats Granvik_, Oct 08 2023
%e A127649 First few rows of the triangle are:
%e A127649 1;
%e A127649 2, 2;
%e A127649 6, 0, 3;
%e A127649 8, 4, 0, 4;
%e A127649 20, 0, 0, 0, 5;
%e A127649 12, 12, 6, 0, 0, 6;
%e A127649 42, 0, 0, 0, 0, 0, 7;
%e A127649 ...
%p A127649 A054523 := proc(n,k) if n mod k = 0 then numtheory[phi](n/k) ; else 0 ; fi ; end: A127649 := proc(n,k) A054523(n,k)*n ; end: for n from 1 to 20 do for k from 1 to n do printf("%d,",A127649(n,k)) ; od: od: # _R. J. Mathar_, Nov 01 2007
%Y A127649 Cf. A127648, A002618, A054523.
%K A127649 nonn,tabl,easy
%O A127649 1,2
%A A127649 _Gary W. Adamson_, Jan 22 2007
%E A127649 More terms from _R. J. Mathar_, Nov 01 2007