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A143343
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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.
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3
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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
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0,3
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COMMENTS
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By the von Stadt-Clausen theorem, the product of the terms in row n is the denominator of the Bernoulli number B_n.
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REFERENCES
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H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
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LINKS
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EXAMPLE
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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,
...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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