|
%I #14 Sep 28 2019 22:20:38
%S 1,1,1,2,1,1,1,4,3,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,5,1,9,1,1,1,1,16,1,1,
%T 1,2,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,32,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,27,1,1,1,1,1
%N a(n) = n/A327501(n), where A327501(n) is the maximum divisor of n that is 1 or not a perfect power.
%C This maximum divisor is given by A327501.
%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).
%H Antti Karttunen, <a href="/A327502/b327502.txt">Table of n, a(n) for n = 1..16383</a>
%H Antti Karttunen, <a href="/A327502/a327502.txt">Data supplement: n, a(n) computed 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/A327501(n).
%e The divisors of 36 that are 1 or not a perfect power are {1, 2, 3, 6, 12, 18}, so a(36) = 36/18 = 2.
%t Table[n/Max[Select[Divisors[n],GCD@@Last/@FactorInteger[#]==1&]],{n,100}]
%o (PARI) A327502(n) = if(n==1, 1, n/vecmax(select(x->((x>1) && !ispower(x)), divisors(n)))); \\ _Antti Karttunen_, Sep 19 2019 (after program given by _Michel Marcus_ for A327501)
%Y See link for additional cross-references.
%Y Cf. A000005, A000961, A001597, A007916, A303386, A327501.
%K nonn,look
%O 1,4
%A _Gus Wiseman_, Sep 16 2019
|
