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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
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; refs; listen; history; text; internal format)
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: A065860 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

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Last modified September 17 07:51 EDT 2021. Contains 347478 sequences. (Running on oeis4.)