A033031 Squarefree kernels of 3-smooth numbers.

1, 2, 3, 2, 6, 2, 3, 6, 2, 6, 6, 3, 2, 6, 6, 6, 2, 6, 3, 6, 6, 2, 6, 6, 6, 6, 3, 2, 6, 6, 6, 6, 6, 2, 6, 6, 3, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 2, 3, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 3, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 3, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 2, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Author

Reinhard Zumkeller, Jun 21 2003

Keywords

• nonn

Examples

			A003586(17) = 64 = 2^6 -> a(17) = 2,
A003586(18) = 72 = 2^3 * 3^2 -> a(18) = 2*3 = 6,
A003586(19) = 81 = 3^4 -> a(19) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A007947, A022328, A022329.

Programs

Mathematica

s = {}; m = 12; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; rad[n_] := Times @@ (First@# & /@ FactorInteger@ n); rad /@ Union[s] (* Amiram Eldar, Jan 29 2020 *)

Formula

a(n) = A007947(A003586(n)).

a(n) = (2*0^(A022328(n)-1)) * (3*0^(A022329(n)-1)) for n>1. - Reinhard Zumkeller, Jul 18 2003

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 6. - Amiram Eldar, Jul 13 2023