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, 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

Offset

1,7

Links

Table of n, a(n) for n=1..105.

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.

Prog

(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.

Sequence in context: A363494 A010110 A116905 * A286562 A185644 A319080

Adjacent sequences: A115076 A115077 A115078 * A115080 A115081 A115082

Keyword

nonn,tabl

Author

Paul D. Hanna, Jan 13 2006

Status

approved