OFFSET
1,1
COMMENTS
It seems to be possible to modify the Redheffer matrix in several ways in order to calculate the Mobius function as determinants. However, the modifications don't seem to follow any clear pattern.
LINKS
E. W. Weisstein, Redheffer Matrix.
FORMULA
T(n,k) = 1 if k=1 or k mod n = 0, otherwise 0. Produces the Redheffer matrix, changes as in example below.
EXAMPLE
Table begins:
1, 1, 1, 1, 1, 1, ...
1, 0, 0, 1, 0, 1, ...
1, 0, 1, 0, 0, 1, ...
1, 0, 0, 1, 1, 0, ...
1, 0, 0, 0, 1, 0, ...
1, 1, 0, 0, 0, 1, ...
where
T(2,2) has been changed from 1 to 0.
T(4,5) has been changed from 0 to 1.
T(6,2) has been changed from 0 to 1.
Values of the first six determinants: 1,-1,-1,0,-1,1.
PROG
(Excel) =if(mod(column(); row())=0; 1; if(column()=1; 1; 0)). Produces the Redheffer matrix.
CROSSREFS
KEYWORD
AUTHOR
Mats Granvik, Jul 20 2008
STATUS
approved