OFFSET
1,6
COMMENTS
LINKS
EXAMPLE
The a(14) = 15 2-edge-connected integer partitions of 14:
(7,7) (6,4,4) (4,4,4,2) (4,4,2,2,2) (4,2,2,2,2,2) (2,2,2,2,2,2,2)
(8,6) (6,6,2) (6,4,2,2) (6,2,2,2,2)
(10,4) (8,4,2) (8,2,2,2)
(12,2) (10,2,2)
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]]]]]]]]];
twoedQ[sys_]:=And[Length[csm[sys]]==1, And@@Table[Length[csm[Delete[sys, i]]]==1, {i, Length[sys]}]];
Table[Length[Select[IntegerPartitions[n], twoedQ[primeMS/@#]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 04 2018
EXTENSIONS
a(42)-a(45) from Jinyuan Wang, Jun 20 2020
STATUS
approved