OFFSET
1,1
COMMENTS
A multiset multisystem is a finite multiset of finite multisets. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part in the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}.
A multiset multisystem is crossing if it contains two parts of the form {{...x...y...},{...z...t...}} with x < z < y < t or z < x < t < y.
MATHEMATICA
croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x<z<y<t||z<x<t<y];
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
setptnQ[bks_]:=UnsameQ@@Join@@bks&&!MemberQ[bks, {}];
Select[Range[10000], And[croXQ[primeMS/@primeMS[#]], setptnQ[primeMS/@primeMS[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 22 2019
STATUS
approved