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A327498 Maximum divisor of n whose prime multiplicities are distinct (A130091).

%I A327498 #26 Apr 02 2022 17:47:49
%S A327498 1,2,3,4,5,3,7,8,9,5,11,12,13,7,5,16,17,18,19,20,7,11,23,24,25,13,27,
%T A327498 28,29,5,31,32,11,17,7,18,37,19,13,40,41,7,43,44,45,23,47,48,49,50,17,
%U A327498 52,53,54,11,56,19,29,59,20,61,31,63,64,13,11,67,68,23
%N A327498 Maximum divisor of n whose prime multiplicities are distinct (A130091).
%C A327498 A number's prime multiplicities are also called its (unsorted) prime signature.
%C A327498 Every positive integer appears a finite number of times in the sequence; a prime p occurs 2^(PrimePi(p) - 1) times. - _David A. Corneth_, Sep 17 2019
%H A327498 David A. Corneth, <a href="/A327498/b327498.txt">Table of n, a(n) for n = 1..10000</a>
%H A327498 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 A327498 a(A130091(n)) = n and a(A130092(n)) < n. - _Ivan N. Ianakiev_, Sep 17 2019
%F A327498 a(n) = n / A327499(n).  - _Antti Karttunen_, Apr 02 2022
%e A327498 The divisors of 60 whose prime multiplicities are distinct are {1, 2, 3, 4, 5, 12, 20}, so a(60) = 20, the largest of these divisors.
%t A327498 Table[Max[Select[Divisors[n],UnsameQ@@Last/@FactorInteger[#]&]],{n,100}]
%o A327498 (PARI) a(n) = {my(m = Map(), f = factor(n), res = 1); forstep(i = #f~, 1, -1, forstep(j = f[i, 2], 1, -1, if(!mapisdefined(m, j), mapput(m, j, j); res*=f[i, 1]^j; next(2)))); res} \\ _David A. Corneth_, Sep 17 2019
%o A327498 (PARI)
%o A327498 A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
%o A327498 A327498(n) = fordiv(n,d,if(A351564(n/d), return(n/d))); \\ _Antti Karttunen_, Apr 02 2022
%Y A327498 See link for additional cross-references.
%Y A327498 Cf. A000005, A000720, A007916, A098859, A124010, A181796, A212168, A255231, A327499, A351564.
%K A327498 nonn,easy
%O A327498 1,2
%A A327498 _Gus Wiseman_, Sep 16 2019