A327499 - OEIS

%I #9 Apr 02 2022 17:47:55

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

%C A number's prime multiplicities are also called its (unsorted) prime signature.

%H Antti Karttunen, <a href="/A327499/b327499.txt">Table of n, a(n) for n = 1..65537</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/A327498(n).

%e The maximum such divisor of 60 is 20, so a(60) = 3.

%t Table[n/Max[Select[Divisors[n],UnsameQ@@Last/@FactorInteger[#]&]],{n,100}]

%o (PARI)

%o A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));

%o A327499(n) = fordiv(n,d,if(A351564(n/d), return(d))); \\ _Antti Karttunen_, Apr 02 2022

%Y See link for additional cross-references.

%Y Cf. A000005, A098859, A124010, A130091, A255231, A327498, A327500, A351564.

%K nonn

%O 1,6

%A _Gus Wiseman_, Sep 16 2019

%E Data section extended up to 105 terms by _Antti Karttunen_, Apr 02 2022