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

Offset: 0

Author

Gary W. Adamson & Mats Granvik, Aug 09 2008

Keywords

• nonn
• tabl

Comments

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

Examples

			The triangle begins:
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,
...
		

References

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

Crossrefs

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

Extensions

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