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%I #13 Dec 19 2023 09:19:51
%S 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,
%T 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,
%U 1,1,1,2,1,1,3,2,1,1,1,5,1,1,1,2,1,1,1
%N Quotient of n over the maximum uniform divisor of n.
%C Requires A071625(n) steps to reach 1, the only fixed point.
%C 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).
%H Amiram Eldar, <a href="/A327528/b327528.txt">Table of n, a(n) for n = 1..10000</a>
%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>.
%F a(n) = n / A327526(n). - _Amiram Eldar_, Dec 19 2023
%e The uniform divisors of 40 are {1, 2, 4, 5, 8, 10}, so a(40) = 40/10 = 4.
%t Table[n/Max[Select[Divisors[n],SameQ@@Last/@FactorInteger[#]&]],{n,100}]
%t 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 *)
%Y See link for additional cross-references.
%Y Cf. A000005, A000961, A005117, A006530, A007947, A071625, A072774, A112798, A327526.
%K nonn
%O 1,12
%A _Gus Wiseman_, Sep 17 2019