login
A033031
Squarefree kernels of 3-smooth numbers.
1
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 21 2003
STATUS
approved