A248470 Put a [+] b = A(A(a) + A(b)), where A = A007913; a(n) is the [+]-sum of binomial(n,i), i=0,...,n.

1, 2, 1, 2, 1, 2, 3, 2, 1, 1, 6, 38, 167, 2095, 1, 2030, 3, 15, 21, 138, 263, 2, 57, 1266, 3470, 7, 145742, 10, 4682335, 110, 38, 618, 366, 83, 3343, 3279, 206555, 215547, 489378, 52010, 21, 5127, 11, 54663, 6203, 5041187, 194, 63038411, 407039, 7602, 2, 2474

Offset

0,2

Comments

By definition, all terms are squarefree (A005117).

Links

Table of n, a(n) for n=0..51.

Example

For n=4, we have binomials: 1,4,6,4,1.
To obtain a(4), we form the sums 1[+]4 = 1[+]1 = 2; 2[+]6 = 2; 2[+]4 = 2[+]1 = 3; 3[+]1=1. So a(4)=1.

Mathematica

a7913[n_]:=a7913[n]=Times@@(#[[1]]^Mod[#[[2]], 2])&[Transpose[FactorInteger[n]]];
ab[x_, y_]:=ab[x, y]=a7913[a7913[x]+a7913[y]];
Table[Fold[ab, First[#], Rest[#]]&[Binomial[n, #]&[Range[0, n]]], {n, 0, 50}] (* Peter J. C. Moses, Oct 27 2014 *)

Prog

(PARI) a(n) = {s = 0; for (i=0, n, s = core(core(binomial(n, i)) + core(s))); s; } \\ Michel Marcus, Nov 14 2014

Crossrefs

Cf. A005117, A007318, A007913.

Sequence in context: A102632 A094076 A089611 * A082067 A082061 A327979

Adjacent sequences: A248467 A248468 A248469 * A248471 A248472 A248473

Keyword

nonn

Author

Vladimir Shevelev, Oct 27 2014

Extensions

More terms from Peter J. C. Moses, Oct 27 2014

Status

approved