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

1,2

Links

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

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

Example

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.

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 *)

Crossrefs

Cf. A003586, A007947, A022328, A022329.

Sequence in context: A183103 A183105 A316608 * A134060 A329282 A197289

Adjacent sequences: A033028 A033029 A033030 * A033032 A033033 A033034

Keyword

nonn

Author

Reinhard Zumkeller, Jun 21 2003

Status

approved