OFFSET
1,1
COMMENTS
The first nonprime term is 195, which is the Heinz number of (6,3,2).
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
An integer partition has edge-connectivity 1 if the prime factorizations of the parts form a connected hypergraph that can be disconnected (or made empty) by removing a single part.
LINKS
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
edgeConn[y_]:=If[Length[csm[primeMS/@y]]!=1, 0, Length[y]-Max@@Length/@Select[Union[Subsets[y]], Length[csm[primeMS/@#]]!=1&]];
Select[Range[100], edgeConn[primeMS[#]]==1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 06 2018
STATUS
approved