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A327528
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Quotient of n over the maximum uniform divisor of n.
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4
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1
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OFFSET
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1,12
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COMMENTS
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Requires A071625(n) steps to reach 1, the only fixed point.
A number is uniform if its prime multiplicities are all equal, meaning it is a power of a squarefree number. Uniform numbers are listed in A072774. The maximum uniform divisor of n is A327526(n).
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LINKS
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FORMULA
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EXAMPLE
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The uniform divisors of 40 are {1, 2, 4, 5, 8, 10}, so a(40) = 40/10 = 4.
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MATHEMATICA
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Table[n/Max[Select[Divisors[n], SameQ@@Last/@FactorInteger[#]&]], {n, 100}]
a[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; n / Max@ Table[(Times @@ p[[Position[e, _?(# >= k &)] // Flatten]])^k, {k, Union[e]}]]; Array[a, 100] (* Amiram Eldar, Dec 19 2023 *)
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CROSSREFS
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See link for additional cross-references.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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