%I #6 Apr 21 2021 10:45:06
%S 0,0,1,0,0,1,0,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,
%T 0,0,0,0,1,0,0,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,
%U 1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0
%N Triangle T(n,k) for 1 <= k <= n read by rows, where T(n,k) = 1 if gcd(n,k) is prime, 0 otherwise.
%F T(n,n) = A010051(n).
%F T(n,1) = 0.
%e The triangle starts
%e 0
%e 0 1
%e 0 0 1
%e 0 1 0 0
%e 0 0 0 0 1
%e 0 1 1 1 0 0
%e 0 0 0 0 0 0 1
%e 0 1 0 0 0 1 0 0
%e 0 0 1 0 0 1 0 0 0
%e 0 1 0 1 1 1 0 1 0 0
%e 0 0 0 0 0 0 0 0 0 0 1
%e 0 1 1 0 0 0 0 0 1 1 0 0
%e 0 0 0 0 0 0 0 0 0 0 0 0 1
%e 0 1 0 1 0 1 1 1 0 1 0 1 0 0
%e 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0
%p A122414 := proc(n,k)
%p if isprime(igcd(n,k)) then
%p 1;
%p else
%p 0;
%p end if;
%p end proc: # _R. J. Mathar_, Apr 21 2021
%o (PARI) {m=14; v=vector(m,x,vector(x)); for(n=1,m,for(k=1,n,if(isprime(gcd(n,k)),v[n][k]=1))); for(n=1,m,for(k=1,n,print1(v[n][k],",")))}
%Y Cf. A010051 (diagonal), A122415 (sub-triangle).
%Y Row sums are in A117494. [From _Klaus Brockhaus_, May 29 2009]
%K nonn,tabl,easy
%O 1,1
%A _Klaus Brockhaus_, Sep 03 2006
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