A248473 - OEIS

%I #30 Dec 25 2023 17:16:08

%S 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 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 5,10,1,1,11,55,165,11,462,462,330,55,11,11,1

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

%C By definition, all terms are squarefree (A005117).

%e For i=8, j=4, we have A(8)=2, A(4)=1, hence b(8,4) = A(binomial(2,1)) = 2.

%e Triangle begins

%e 1

%e 1   1

%e 1   2   1

%e 1   3   3   1

%e 1   1   0   0   1

%e 1   5  10  10   5   1

%e 1   6  15   5   6   6   1

%e 1   7  21  35   7  21   7   1

%e 1   2   1   0   2   0   0   0   1

%e 1   1   0   0   1   0   0   0   0   1

%e 1  10   5  30  10   7 210  30   5  10  1

%e ..........................................

%t a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]],2])&[Transpose[FactorInteger[n]]];

%t Flatten[Table[a7913[Binomial[a7913[m],a7913[k]]],{m,0,10},{k,0,m}]] (* _Peter J. C. Moses_, Oct 27 2014 *)

%Y Cf. A005117, A007318, A007913, A248470.

%K nonn,tabl

%O 0,5

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 27 2014