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

Author

Reinhard Zumkeller, Jan 01 2002

Keywords

• nonn
• easy

Comments

This sequence is not the same as A046660.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Haskell

a066301 1 = 0
a066301 n = a051903 n - 1  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

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

PARI

a(n)=if(n>1, vecmax(factor(n)[,2])-1, 0) \\ Charles R Greathouse IV, Jul 15 2013

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