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A127638 A054525 * A127640, where A127640 = infinite lower triangular matrix with the sequence of primes in the main diagonal and the rest zeros.

%I A127638 #8 Feb 14 2022 23:33:14
%S A127638 2,-2,3,-2,0,5,0,-3,0,7,-2,0,0,0,11,2,-3,-5,0,0,13,-2,0,0,0,0,0,17,0,
%T A127638 0,0,-7,0,0,0,19,0,0,-5,0,0,0,0,0,23,2,-3,0,0,-11,0,0,0,0,29,-2,0,0,0,
%U A127638 0,0,0,0,0,0,31,0,3,0,-7,0,-13,0,0,0,0,0,37,-2,0,0,0,0,0,0,0,0,0,0,0,41,2,-3,0,0,0,0,-17,0,0,0,0,0,0,43,2,0,-5,0,-11,0,0
%N A127638 A054525 * A127640, where A127640 = infinite lower triangular matrix with the sequence of primes in the main diagonal and the rest zeros.
%C A127638 Right diagonal = primes: (2, 3, 5, 7, ...). Row sums = the Mobius transform of primes, A007444: (2, 1, 3, 4, 9, 7, ...).
%e A127638 First few rows of the triangle:
%e A127638    2;
%e A127638   -2,  3;
%e A127638   -2,  0,  5;
%e A127638    0, -3,  0, 7;
%e A127638   -2,  0,  0, 0, 11;
%e A127638    2, -3, -5, 0,  0, 13;
%e A127638   ...
%p A127638 A054525 := proc(n,k) if n mod k = 0 then numtheory[mobius](n/k) ; else 0 ; fi ; end: A127648 := proc(n,k) A054525(n,k)*ithprime(k) ; end: for n from 1 to 16 do for k from 1 to n do printf("%d,", A127648(n,k)) ; od ; od ; # _R. J. Mathar_, Mar 14 2007
%Y A127638 Cf. A007444, A054525, A127639.
%K A127638 tabl,easy,sign
%O A127638 1,1
%A A127638 _Gary W. Adamson_, Jan 21 2007
%E A127638 More terms from _R. J. Mathar_, Mar 14 2007