cp's OEIS Frontend

A327528 Quotient of n over the maximum uniform divisor of n.

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