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

Author

Reinhard Zumkeller, Jul 29 2002

Keywords

• nonn
• look

Comments

a(n)=1 iff n is squarefree.

Links

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

Crossrefs

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

Programs

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 *)

Formula

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