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A066301
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a(n) = 0 if n is squarefree, otherwise 1 + a(n/rad(n)) where rad = A007947 (squarefree kernel).
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4
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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
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OFFSET
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1,8
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COMMENTS
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This sequence is not the same as A046660.
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LINKS
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FORMULA
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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
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EXAMPLE
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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.
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MATHEMATICA
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a[n_] := Max[FactorInteger[n][[;; , 2]]] - 1; Array[a, 100] (* Amiram Eldar, Jan 05 2024 *)
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PROG
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(Haskell)
a066301 1 = 0
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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