OFFSET
1,2
COMMENTS
First differs from A322551 in having 377.
Also products of distinct elements of A322551.
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 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}}.
Covering means there are no isolated vertices, i.e., the vertex set is the union of the edge set.
EXAMPLE
The sequence of edge sets together with their MM-numbers begins:
1: {}
13: {{1,2}}
29: {{1,3}}
43: {{1,4}}
47: {{2,3}}
73: {{2,4}}
79: {{1,5}}
101: {{1,6}}
137: {{2,5}}
139: {{1,7}}
149: {{3,4}}
163: {{1,8}}
167: {{2,6}}
199: {{1,9}}
233: {{2,7}}
257: {{3,5}}
269: {{2,8}}
271: {{1,10}}
293: {{1,11}}
313: {{3,6}}
347: {{2,9}}
373: {{1,12}}
377: {{1,2},{1,3}}
389: {{4,5}}
421: {{1,13}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], And[SquareFreeQ[#], And@@(And[SquareFreeQ[#], Length[primeMS[#]]==2]&/@primeMS[#])]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved