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%I #12 Dec 19 2023 09:20:00
%S 1,2,3,4,5,6,7,8,9,10,11,6,13,14,15,16,17,9,19,10,21,22,23,8,25,26,27,
%T 14,29,30,31,32,33,34,35,36,37,38,39,10,41,42,43,22,15,46,47,16,49,25,
%U 51,26,53,27,55,14,57,58,59,30,61,62,21,64,65,66,67,34
%N Maximum uniform divisor of n.
%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 number of uniform divisors of n is A327527(n).
%H Amiram Eldar, <a href="/A327526/b327526.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 / A327528(n). - _Amiram Eldar_, Dec 19 2023
%e The uniform divisors of 40 are {1, 2, 4, 5, 8, 10}, so a(40) = 10.
%t Table[Max[Select[Divisors[n],SameQ@@Last/@FactorInteger[#]&]],{n,100}]
%t a[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; 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, A327528.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 16 2019
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