OFFSET
1,2
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.
LINKS
EXAMPLE
The sequence of all connected sets of multisets together with their MM-numbers (A302242) begins:
1: {}
2: {{}}
3: {{1}}
5: {{2}}
7: {{1,1}}
11: {{3}}
13: {{1,2}}
17: {{4}}
19: {{1,1,1}}
21: {{1},{1,1}}
23: {{2,2}}
29: {{1,3}}
31: {{5}}
37: {{1,1,2}}
39: {{1},{1,2}}
41: {{6}}
43: {{1,4}}
47: {{2,3}}
53: {{1,1,1,1}}
57: {{1},{1,1,1}}
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]]]]]]]]];
Select[Range[100], SquareFreeQ[#]&&Length[zsm[primeMS[#]]]<=1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 20 2019
STATUS
approved