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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.

%I A143343 #19 Aug 10 2019 18:42:22
%S A143343 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,
%T A143343 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,
%U A143343 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
%N 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.
%C A143343 By the von Stadt-Clausen theorem, the product of the terms in row n is the denominator of the Bernoulli number B_n.
%D A143343 H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
%e A143343 The triangle begins:
%e A143343 1,
%e A143343 1,2,
%e A143343 1,2,3,
%e A143343 1,1,1,1,
%e A143343 1,2,3,1,5,
%e A143343 1,1,1,1,1,1,
%e A143343 1,2,3,1,1,1,7,
%e A143343 1,1,1,1,1,1,1,1,
%e A143343 1,2,3,1,5,1,1,1,1,
%e A143343 1,1,1,1,1,1,1,1,1,1,
%e A143343 1,2,3,1,1,1,1,1,1,1,11,
%e A143343 1,1,1,1,1,1,1,1,1,1,1,1,
%e A143343 1,2,3,1,5,1,7,1,1,1,1,1,13,
%e A143343 1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%e A143343 ...
%Y A143343 Cf. A002445, A027642, A080092, A127093, A138239, A138243, A176079, A191904, A191910.
%K A143343 nonn,tabl
%O A143343 0,3
%A A143343 _Gary W. Adamson_ & _Mats Granvik_, Aug 09 2008
%E A143343 Entry revised by _N. J. A. Sloane_, Aug 10 2019