A073354 Binomial coefficient ( n, squarefree kernel(n) ).

1, 1, 1, 6, 1, 1, 1, 28, 84, 1, 1, 924, 1, 1, 1, 120, 1, 18564, 1, 184756, 1, 1, 1, 134596, 53130, 1, 2925, 40116600, 1, 1, 1, 496, 1, 1, 1, 1947792, 1, 1, 1, 847660528, 1, 1, 1, 2104098963720, 344867425584, 1, 1, 12271512, 85900584, 10272278170, 1

Offset

1,4

Comments

a(n)=1 iff n is squarefree.

Links

Robert Israel, Table of n, a(n) for n = 1..3315

Formula

a(n) = binomial(n, A007947(n)).

Maple

f:= proc(n) local k;
  k:= convert(numtheory:-factorset(n), `*`);
  binomial(n, k)
end proc:
map(f, [$1..60]); # Robert Israel, May 07 2021

Mathematica

a[n_] := Binomial[n, Times @@ FactorInteger[n][[All, 1]]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, May 11 2023 *)

Crossrefs

Cf. A007947, A005117, A073353, A066503, A064549, A003557.

Sequence in context: A050449 A316623 A108131 * A358461 A197420 A128423

Adjacent sequences: A073351 A073352 A073353 * A073355 A073356 A073357

Keyword

nonn,look

Author

Reinhard Zumkeller, Jul 29 2002

Status

approved