|
Search: id:A115079
|
|
|
| A115079 |
|
Matrix log of triangle A051731, where nonzero elements in the matrix log are all unit fractions and represented here by the denominators, with zero elements remaining zero. |
|
+0
1
|
|
| 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 2, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
1,7
|
|
|
EXAMPLE
|
This triangle is defined by:
* T(n,k) = A100995(n/k) if k|n, 0 otherwise.
Sequence A100995 is defined by:
* A100995(n) = m if n = p^m for some prime p, 0 otherwise.
Triangle A054525 equals A051731^-1 and is defined by:
* A054525(n,k) = MoebiusMu(n/k) if k|n, 0 otherwise.
Triangle A051731 is defined by:
* A051731(n,k) = 1 if k|n, 0 otherwise.
The matrix log of triangle A051731 begins:
0;
1, 0;
1, 0, 0;
1/2, 1, 0, 0;
1, 0, 0, 0, 0;
0, 1, 1, 0, 0, 0;
1, 0, 0, 0, 0, 0, 0;
1/3, 1/2, 0, 1, 0, 0, 0, 0;
1/2, 0, 1, 0, 0, 0, 0, 0, 0;
0, 1, 0, 0, 1, 0, 0, 0, 0, 0;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 1/2, 1, 0, 1, 0, 0, 0, 0, 0, 0;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0;
0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
1/4, 1/3, 0, 1/2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; ...
where all nonzero elements are positive unit fractions.
|
|
PROGRAM
|
(PARI) T(n, k)=if(n%k==0, if(#(factor(n/k)~)==1, factor(n/k)[1, 2], 0), 0)
|
|
CROSSREFS
|
Cf. A051731, A100995, A054525.
Adjacent sequences: A115076 A115077 A115078 this_sequence A115080 A115081 A115082
Sequence in context: A065860 A010110 A116905 this_sequence A025435 A081221 A103840
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jan 13 2006
|
|
|
Search completed in 0.002 seconds
|
