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A140579 Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.

%I A140579 #10 Feb 16 2019 18:15:09
%S A140579 1,0,2,0,0,3,0,0,0,2,0,0,0,0,5,0,0,0,0,0,1,0,0,0,0,0,0,7,0,0,0,0,0,0,
%T A140579 0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,11,0,0,
%U A140579 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,13
%N A140579 Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.
%C A140579 A140579 * [1, 2, 3,...] = A140580.
%C A140579 (A140579)^(-1) * [1, 2, 3,...] = A048671: (1, 1, 1, 2, 1, 6, 1, 4, 3, 10,...).
%C A140579 A008683 = A140579^(-1) * A140664. - _Gary W. Adamson_, May 20 2008
%H A140579 G. C. Greubel, <a href="/A140579/b140579.txt">Rows n=1..100 of triangle, flattened</a>
%F A140579 Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.
%F A140579 Infinite lower triangular matrix with A014963 (1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11,...) in the main diagonal and the rest zeros.
%e A140579 First few rows of the triangle are:
%e A140579 1;
%e A140579 0, 2;
%e A140579 0, 0, 3;
%e A140579 0, 0, 0, 2;
%e A140579 0, 0, 0, 0, 5;
%e A140579 0, 0, 0, 0, 0, 1;
%e A140579 0, 0, 0, 0, 0, 0, 7;
%e A140579 ...
%t A140579 Table[If[k != n ,0,Exp[MangoldtLambda[n]]], {n,1,12}, {k,1,n}]//Flatten (* _G. C. Greubel_, Feb 16 2019 *)
%o A140579 (PARI) {T(n,k) = if(n==1, 1, gcd(vector(n-1, k, binomial(n, k)))*0^(n-k))};
%o A140579 for(n=1,12, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Feb 16 2019
%o A140579 (Sage)
%o A140579 def T(n,k): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*0^(n-k)
%o A140579 [[T(n,k) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, Feb 16 2019
%Y A140579 Cf. A014963, A140580, A048671.
%Y A140579 Cf. A008683, A140664.
%K A140579 nonn,tabl
%O A140579 1,3
%A A140579 _Gary W. Adamson_ and _Mats Granvik_, May 17 2008