OFFSET
1,2
COMMENTS
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, which is the union of this sequence without 1.
Also the maximum MM-number (A302242) of a connected subset of the multiset of multisets with MM-number n.
LINKS
FORMULA
If n is in A305078, then a(n) = n.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
zsm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], GCD@@s[[#]]>1&]}, If[c=={}, s, zsm[Sort[Append[Delete[s, List/@c[[1]]], LCM@@s[[c[[1]]]]]]]]];
Table[Max[Select[Divisors[n], Length[zsm[primeMS[#]]]<=1&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 05 2019
STATUS
approved