A143343 - OEIS

A143343

Triangle T(n,k) (n>=0, 1<=k<=n+1) read by rows: T(n,1)=1 for n>=0, T(1,2)=2. If n>=3 is odd then T(n,k)=1 for all k. If n>=3 is even then if k is prime and k-1 divides n then T(n,k)=k, otherwise T(n,k)=1.

1, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 2, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 5, 1, 7, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

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OFFSET

0,3

COMMENTS

By the von Stadt-Clausen theorem, the product of the terms in row n is the denominator of the Bernoulli number B_n.

REFERENCES

H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.

LINKS

Table of n, a(n) for n=0..104.

EXAMPLE

The triangle begins:

1,2,

1,2,3,

1,1,1,1,

1,2,3,1,5,

1,1,1,1,1,1,

1,2,3,1,1,1,7,

1,1,1,1,1,1,1,1,

1,2,3,1,5,1,1,1,1,

1,1,1,1,1,1,1,1,1,1,

1,2,3,1,1,1,1,1,1,1,11,

1,1,1,1,1,1,1,1,1,1,1,1,

1,2,3,1,5,1,7,1,1,1,1,1,13,

1,1,1,1,1,1,1,1,1,1,1,1,1,1,

...

CROSSREFS

Cf. A002445, A027642, A080092, A127093, A138239, A138243, A176079, A191904, A191910.

Sequence in context: A167684 A094646 A124448 * A138243 A273136 A273137

Adjacent sequences: A143340 A143341 A143342 * A143344 A143345 A143346

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson & Mats Granvik, Aug 09 2008

EXTENSIONS

Entry revised by N. J. A. Sloane, Aug 10 2019

STATUS

approved