OFFSET
1,1
EXAMPLE
The terms together with their prime indices begin:
30: {1,2,3}
36: {1,1,2,2}
42: {1,2,4}
60: {1,1,2,3}
66: {1,2,5}
70: {1,3,4}
78: {1,2,6}
84: {1,1,2,4}
90: {1,2,2,3}
100: {1,1,3,3}
For example, the multiset partitions of the prime indices of 36 include {{1},{1,2,2}} and {{2},{1,1,2}}, which are isomorphic, so 36 is in the sequence.
MATHEMATICA
brute[m_]:=If[Union@@m!={}&&Union@@m!=Range[Max@@Flatten[m]], brute[m/.Rule@@@Table[{(Union@@m)[[i]], i}, {i, Length[Union@@m]}]], First[Sort[brute[m, 1]]]]; brute[m_, 1]:=Table[Sort[Sort/@(m/.Rule@@@Table[{i, p[[i]]}, {i, Length[p]}])], {p, Permutations[Union@@m]}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !UnsameQ@@brute/@mps[primeMS[#]]&]
CROSSREFS
The complement is A357873.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 18 2022
STATUS
approved