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A248473 Triangle of numbers b(i,j) = A(binomial(A(i), A(j))), where A = A007913, with the convention that A(0)=0.

%I A248473 #30 Dec 25 2023 17:16:08
%S A248473 1,1,1,1,2,1,1,3,3,1,1,1,0,0,1,1,5,10,10,5,1,1,6,15,5,6,6,1,1,7,21,35,
%T A248473 7,21,7,1,1,2,1,0,2,0,0,0,1,1,1,0,0,1,0,0,0,0,1,1,10,5,30,10,7,210,30,
%U A248473 5,10,1,1,11,55,165,11,462,462,330,55,11,11,1
%N A248473 Triangle of numbers b(i,j) = A(binomial(A(i), A(j))), where A = A007913, with the convention that A(0)=0.
%C A248473 By definition, all terms are squarefree (A005117).
%e A248473 For i=8, j=4, we have A(8)=2, A(4)=1, hence b(8,4) = A(binomial(2,1)) = 2.
%e A248473 Triangle begins
%e A248473 1
%e A248473 1   1
%e A248473 1   2   1
%e A248473 1   3   3   1
%e A248473 1   1   0   0   1
%e A248473 1   5  10  10   5   1
%e A248473 1   6  15   5   6   6   1
%e A248473 1   7  21  35   7  21   7   1
%e A248473 1   2   1   0   2   0   0   0   1
%e A248473 1   1   0   0   1   0   0   0   0   1
%e A248473 1  10   5  30  10   7 210  30   5  10  1
%e A248473 ..........................................
%t A248473 a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]],2])&[Transpose[FactorInteger[n]]];
%t A248473 Flatten[Table[a7913[Binomial[a7913[m],a7913[k]]],{m,0,10},{k,0,m}]] (* _Peter J. C. Moses_, Oct 27 2014 *)
%Y A248473 Cf. A005117, A007318, A007913, A248470.
%K A248473 nonn,tabl
%O A248473 0,5
%A A248473 _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 27 2014