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A066301 a(n) = 0 if n is squarefree, otherwise 1 + a(n/rad(n)) where rad = A007947 (squarefree kernel). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
This sequence is not the same as A046660.
LINKS
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
Sequence in context: A366988 A280827 A103840 * A046660 A368251 A183094
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jan 01 2002
STATUS
approved

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)