login
A054525 * A127640, where A127640 = infinite lower triangular matrix with the sequence of primes in the main diagonal and the rest zeros.
3

%I #8 Feb 14 2022 23:33:14

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

%C Right diagonal = primes: (2, 3, 5, 7, ...). Row sums = the Mobius transform of primes, A007444: (2, 1, 3, 4, 9, 7, ...).

%e First few rows of the triangle:

%e 2;

%e -2, 3;

%e -2, 0, 5;

%e 0, -3, 0, 7;

%e -2, 0, 0, 0, 11;

%e 2, -3, -5, 0, 0, 13;

%e ...

%p 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 Cf. A007444, A054525, A127639.

%K tabl,easy,sign

%O 1,1

%A _Gary W. Adamson_, Jan 21 2007

%E More terms from _R. J. Mathar_, Mar 14 2007