cp's OEIS Frontend

A327395 Quotient of n over the maximum connected divisor of n.

%I A327395 #5 Sep 16 2019 12:38:28
%S A327395 1,1,1,2,1,2,1,4,1,2,1,4,1,2,3,8,1,2,1,4,1,2,1,8,1,2,1,4,1,6,1,16,3,2,
%T A327395 5,4,1,2,1,8,1,2,1,4,5,2,1,16,1,2,3,4,1,2,5,8,1,2,1,12,1,2,1,32,1,6,1,
%U A327395 4,3,10,1,8,1,2,3,4,7,2,1,16,1,2,1,4,5
%N A327395 Quotient of n over the maximum connected divisor of n.
%C A327395 Requires A305079(n) steps to reach 1, the only fixed point.
%C A327395 A number n with prime factorization n = prime(m_1)^s_1 * ... * prime(m_k)^s_k is connected if the simple labeled graph with vertex set {m_1,...,m_k} and edges between any two vertices with a common divisor greater than 1 is connected. Connected numbers are listed in A305078.
%H A327395 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 A327395 a(n) = n/A327076(n).
%t A327395 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327395 zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Sort[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
%t A327395 maxcon[n_]:=Max[Select[Divisors[n],Length[zsm[primeMS[#]]]<=1&]];
%t A327395 Table[n/maxcon[n],{n,100}]
%Y A327395 See link for additional crossrefs.
%Y A327395 Positions of 1's are A305078.
%Y A327395 Positions of 2's are 2 * A305078.
%Y A327395 Cf. A000005, A304716, A304714, A305079, A327076.
%K A327395 nonn
%O A327395 1,4
%A A327395 _Gus Wiseman_, Sep 15 2019