cp's OEIS Frontend

A336617 a(n) = n!/d where d = A336616(n) is the maximum divisor of n! with distinct prime multiplicities.

%I A336617 #20 Sep 02 2020 23:06:04
%S A336617 1,1,1,2,1,3,1,5,5,5,1,7,7,77,275,11,11,143,143,2431,2431,2431,221,
%T A336617 4199,4199,4199,39083,39083,39083,898909,898909,26068361,26068361,
%U A336617 215441,2141737,2141737,2141737,66393847,1009885357,7953594143,7953594143,294282983291
%N A336617 a(n) = n!/d where d = A336616(n) is the maximum divisor of n! with distinct prime multiplicities.
%C A336617 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.
%H A336617 Jinyuan Wang, <a href="/A336617/b336617.txt">Table of n, a(n) for n = 0..1000</a>
%H A336617 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 A336617 a(n) = A327499(n!).
%e A336617 The maximum divisor of 13! with distinct prime multiplicities is 80870400, so a(13) = 13!/80870400 = 77.
%t A336617 Table[n!/Max@@Select[Divisors[n!],UnsameQ@@Last/@If[#==1,{},FactorInteger[#]]&],{n,0,15}]
%Y A336617 A327499 is the non-factorial generalization, with quotient A327498.
%Y A336617 A336414 counts these divisors.
%Y A336617 A336616 is the maximum divisor d.
%Y A336617 A336619 is the version for equal prime multiplicities.
%Y A336617 A130091 lists numbers with distinct prime multiplicities.
%Y A336617 A181796 counts divisors with distinct prime multiplicities.
%Y A336617 A336415 counts divisors of n! with equal prime multiplicities.
%Y A336617 Cf. A000005, A098859, A124010, A336424, A336500, A336568.
%Y A336617 Factorial numbers: A000142, A007489, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A327500, A336416, A336618.
%K A336617 nonn
%O A336617 0,4
%A A336617 _Gus Wiseman_, Jul 29 2020
%E A336617 More terms from _Jinyuan Wang_, Jul 31 2020