OFFSET
1,2
COMMENTS
EXAMPLE
The terms together with their prime indices of binary indices begin:
1: {{}}
2: {{1}}
4: {{2}}
8: {{1,1}}
16: {{3}}
32: {{1,2}}
40: {{1,1},{1,2}}
64: {{4}}
128: {{1,1,1}}
160: {{1,2},{1,1,1}}
256: {{2,2}}
288: {{1,2},{2,2}}
296: {{1,1},{1,2},{2,2}}
416: {{1,2},{1,1,1},{2,2}}
512: {{1,3}}
520: {{1,1},{1,3}}
544: {{1,2},{1,3}}
552: {{1,1},{1,2},{1,3}}
640: {{1,1,1},{1,3}}
672: {{1,2},{1,1,1},{1,3}}
800: {{1,2},{2,2},{1,3}}
808: {{1,1},{1,2},{2,2},{1,3}}
928: {{1,2},{1,1,1},{2,2},{1,3}}
MATHEMATICA
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], stableQ[bpe[#], Divisible]&&connectedQ[prix/@bpe[#]]&]
CROSSREFS
A001187 counts connected graphs.
A007718 counts non-isomorphic connected multiset partitions.
A048143 counts connected antichains of sets.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2024
STATUS
approved