A066301 a(n) = 0 if n is squarefree, otherwise 1 + a(n/rad(n)) where rad = A007947 (squarefree kernel).

0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 3, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 1, 5, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 3, 3, 0, 0, 1, 0, 0, 0, 2, 0, 1

Offset

1,8

Comments

This sequence is not the same as A046660.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A051903(n)-1 for n > 1, a(1) = 0.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A033150 - 1 = 0.705211... . - Amiram Eldar, Jan 05 2024

Example

a(24) = 1 + a(24/rad(24)) = 1 + a(24/6) = 1 + a(4) = 1 + (1+a(4/rad(4))) = 1 + (1+a(4/2)) = 2 + a(2) = 2 + 0 = 2.

Mathematica

a[n_] := Max[FactorInteger[n][[;; , 2]]] - 1; Array[a, 100] (* Amiram Eldar, Jan 05 2024 *)

Prog

(PARI) a(n)=if(n>1, vecmax(factor(n)[, 2])-1, 0) \\ Charles R Greathouse IV, Jul 15 2013
(Haskell)
a066301 1 = 0
a066301 n = a051903 n - 1  -- Reinhard Zumkeller, Jul 23 2013

Crossrefs

Cf. A005117, A007947, A003557, A008966, A033150, A046660, A051903.

Sequence in context: A366988 A280827 A103840 * A046660 A368251 A183094

Adjacent sequences: A066298 A066299 A066300 * A066302 A066303 A066304

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 01 2002

Status

approved