A327398 Maximum connected squarefree divisor of n.

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5, 21, 11, 23, 3, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 39, 5, 41, 21, 43, 11, 5, 23, 47, 3, 7, 5, 17, 13, 53, 3, 11, 7, 57, 29, 59, 5, 61, 31, 21, 2, 65, 11, 67, 17, 23, 7, 71, 3, 73, 37

Offset: 1

Author

Gus Wiseman, Oct 20 2019

Keywords

• nonn

Comments

A squarefree number with prime factorization prime(m_1) * ... * prime(m_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.

Examples

			The connected squarefree divisors of 189 are {1, 3, 7, 21}, so a(189) = 21.
		

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

The maximum connected divisor of n is A327076(n).

The maximum squarefree divisor of n is A007947(n).

Connected numbers are A305078.

Connected squarefree numbers are A328513.

Cf. A000005, A001221, A302242, A302494, A304714, A305079, A327656, A328514.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
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]]]]]]]]];
Table[Max[Select[Divisors[n],SquareFreeQ[#]&&Length[zsm[primeMS[#]]]<=1&]],{n,100}]