%I #18 Jan 17 2024 17:24:40
%S 1,2,3,2,5,6,7,2,3,10,11,12,13,14,15,2,17,18,19,20,21,22,23,24,5,26,3,
%T 28,29,30,31,2,33,34,35,18,37,38,39,40,41,42,43,44,45,46,47,48,7,50,
%U 51,52,53,54,55,56,57,58,59,60,61,62,63,2,65,66,67,68,69
%N Maximum divisor of n that is 1 or not a perfect power.
%C First differs from A052410 at a(36) = 18, A052410(36) = 6.
%C The number of divisors that are 1 or not a perfect power is given by A327502.
%C A multiset is aperiodic if its multiplicities are relatively prime. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Heinz numbers of aperiodic multisets are numbers that are not perfect powers (A007916).
%C a(n) = n iff n is in A175082. - _Bernard Schott_, Sep 20 2019
%H Andrew Howroyd, <a href="/A327501/b327501.txt">Table of n, a(n) for n = 1..10000</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>
%e The divisors of 36 that are not perfect powers are {1, 2, 3, 6, 12, 18}, so a(36) = 18.
%t Table[Max[Select[Divisors[n],GCD@@Last/@FactorInteger[#]==1&]],{n,100}]
%o (PARI) isp(n) = !ispower(n) && (n>1); \\ A007916
%o a(n) = if (n==1, 1, vecmax(select(x->isp(x), divisors(n)))); \\ _Michel Marcus_, Sep 18 2019
%o (Magma) [1] cat [Max([d:d in Divisors(n)| d gt 1 and not IsPower(d)]):n in [2..70]]; // _Marius A. Burtea_, Sep 20 2019
%Y See link for additional cross-references.
%Y Cf. A000005, A000961, A001597, A007916, A303386, A327502.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 16 2019