A127569 Triangle read by rows: product of the Mobius matrix A054525 by the diagonal matrix diag(A000203(n)).

1, -1, 3, -1, 0, 4, 0, -3, 0, 7, -1, 0, 0, 0, 6, 1, -3, -4, 0, 0, 12, -1, 0, 0, 0, 0, 0, 8, 0, 0, 0, -7, 0, 0, 0, 15, 0, 0, -4, 0, 0, 0, 0, 0, 13, 1, -3, 0, 0, -6, 0, 0, 0, 0, 18, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 3, 0, -7, 0, -12, 0, 0, 0, 0, 0, 28, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 1, -3, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 24, 1, 0, -4, 0, -6, 0, 0, 0, 0, 0

Offset

1,3

Comments

Left column = mu(n), A008683; right border = sigma(n), A000203; row sums = n.

The definition of Mobius transform is extended to matrices here in the sense of "left multiplication by the Mobius matrix A054525". - R. J. Mathar, Oct 02 2007

Links

Table of n, a(n) for n=1..115.

Formula

T(n,k)=A054525(n,k)*A000203(k). - R. J. Mathar, Oct 02 2007

Example

First few rows of the triangle are:
1;
-1, 3;
-1, 0, 4;
0, -3, 0, 7;
-1, 0, 0, 0, 6;
1, -3, -4, 0, 0, 12;
...

Maple

A000203T := proc(n, k) if n = k then numtheory[sigma](n) ; else 0 ; fi ; end: A054525 := proc(n, k) if n < 1 or k > n or n mod k <> 0 then 0; else numtheory[mobius](n/k) ; fi ; end: A127569 := proc(n, k) add(A054525(n, i)*A000203T(i, k), i=1..n) ; end: for n from 1 to 15 do for k from 1 to n do printf("%a, ", A127569(n, k)) ; od: od: # R. J. Mathar, Oct 02 2007

Crossrefs

Cf. A054525, A000203, A008683.

Sequence in context: A159059 A340262 A346369 * A117372 A127570 A340583

Adjacent sequences: A127566 A127567 A127568 * A127570 A127571 A127572

Keyword

tabl,sign

Author

Gary W. Adamson, Jan 19 2007

Extensions

Missing comma corrected by Naruto Canada, Aug 26 2007

More terms from R. J. Mathar, Oct 02 2007

Status

approved