OFFSET
1,2
COMMENTS
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 of 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}}.
LINKS
Wikipedia, Hypergraph
EXAMPLE
The sequence of terms together with their multiset multisystems begins:
1: {}
13: {{1,2}}
113: {{1,2,3}}
169: {{1,2},{1,2}}
377: {{1,2},{1,3}}
611: {{1,2},{2,3}}
1291: {{1,2,3,4}}
1363: {{1,3},{2,3}}
1469: {{1,2},{1,2,3}}
1937: {{1,2},{3,4}}
2021: {{1,4},{2,3}}
2117: {{1,3},{2,4}}
2197: {{1,2},{1,2},{1,2}}
3277: {{1,3},{1,2,3}}
4537: {{1,2},{1,3,4}}
4859: {{1,4},{1,2,3}}
4901: {{1,2},{1,2},{1,3}}
5249: {{1,3},{1,2,4}}
5311: {{2,3},{1,2,3}}
7423: {{1,2},{2,3,4}}
7943: {{1,2},{1,2},{2,3}}
8249: {{2,4},{1,2,3}}
8507: {{2,3},{1,2,4}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
normQ[sys_]:=Or[Length[sys]==0, Union@@sys==Range[Max@@Max@@sys]];
Select[Range[10000], And[normQ[primeMS/@primeMS[#]], And@@(And[SquareFreeQ[#], PrimeOmega[#]>1]&/@primeMS[#])]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 13 2018
STATUS
approved