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

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, 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, 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

Offset: 1

Author

Gary W. Adamson, Jan 21 2007

Keywords

• tabl
• easy
• sign

Comments

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

Examples

			First few rows of the triangle:
   2;
  -2,  3;
  -2,  0,  5;
   0, -3,  0, 7;
  -2,  0,  0, 0, 11;
   2, -3, -5, 0,  0, 13;
  ...
		

Crossrefs

Cf. A007444, A054525, A127639.

Programs

Maple

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

Extensions

More terms from R. J. Mathar, Mar 14 2007