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A327499 Quotient of n over the maximum divisor of n whose prime multiplicities are distinct.

%I A327499 #9 Apr 02 2022 17:47:55
%S A327499 1,1,1,1,1,2,1,1,1,2,1,1,1,2,3,1,1,1,1,1,3,2,1,1,1,2,1,1,1,6,1,1,3,2,
%T A327499 5,2,1,2,3,1,1,6,1,1,1,2,1,1,1,1,3,1,1,1,5,1,3,2,1,3,1,2,1,1,5,6,1,1,
%U A327499 3,10,1,1,1,2,1,1,7,6,1,1,1,2,1,3,5,2,3,1,1,2,7,1,3,2,5,1,1,1,1,2,1,6,1,1,15
%N A327499 Quotient of n over the maximum divisor of n whose prime multiplicities are distinct.
%C A327499 A number's prime multiplicities are also called its (unsorted) prime signature.
%H A327499 Antti Karttunen, <a href="/A327499/b327499.txt">Table of n, a(n) for n = 1..65537</a>
%H A327499 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 A327499 a(n) = n/A327498(n).
%e A327499 The maximum such divisor of 60 is 20, so a(60) = 3.
%t A327499 Table[n/Max[Select[Divisors[n],UnsameQ@@Last/@FactorInteger[#]&]],{n,100}]
%o A327499 (PARI)
%o A327499 A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
%o A327499 A327499(n) = fordiv(n,d,if(A351564(n/d), return(d))); \\ _Antti Karttunen_, Apr 02 2022
%Y A327499 See link for additional cross-references.
%Y A327499 Cf. A000005, A098859, A124010, A130091, A255231, A327498, A327500, A351564.
%K A327499 nonn
%O A327499 1,6
%A A327499 _Gus Wiseman_, Sep 16 2019
%E A327499 Data section extended up to 105 terms by _Antti Karttunen_, Apr 02 2022