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

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

Offset

0,5

Comments

By definition, all terms are squarefree (A005117).

Links

Table of n, a(n) for n=0..77.

Example

For i=8, j=4, we have A(8)=2, A(4)=1, hence b(8,4) = A(binomial(2,1)) = 2.
Triangle begins
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   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   5  10  1
..........................................

Mathematica

a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]], 2])&[Transpose[FactorInteger[n]]];
Flatten[Table[a7913[Binomial[a7913[m], a7913[k]]], {m, 0, 10}, {k, 0, m}]] (* Peter J. C. Moses, Oct 27 2014 *)

Crossrefs

Cf. A005117, A007318, A007913, A248470.

Sequence in context: A129571 A180180 A034931 * A307116 A212626 A090402

Adjacent sequences: A248470 A248471 A248472 * A248474 A248475 A248476

Keyword

nonn,tabl

Author

Vladimir Shevelev and Peter J. C. Moses, Oct 27 2014

Status

approved