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A329556
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Smallest MM-number of a set of n sets with no singletons.
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5
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OFFSET
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0,2
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COMMENTS
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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 of multisets 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 of multisets with MM-number 78 is {{},{1},{1,2}}.
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LINKS
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EXAMPLE
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The sequence of terms together with their corresponding systems begins:
1: {}
2: {{}}
26: {{},{1,2}}
754: {{},{1,2},{1,3}}
32422: {{},{1,2},{1,3},{1,4}}
1523834: {{},{1,2},{1,3},{1,4},{2,3}}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
dae=Select[Range[100000], SquareFreeQ[#]&&And@@SquareFreeQ/@primeMS[#]&&FreeQ[primeMS[#], _?PrimeQ]&];
Table[dae[[Position[PrimeOmega/@dae, k][[1, 1]]]], {k, First[Split[Union[PrimeOmega/@dae], #2==#1+1&]]}]
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CROSSREFS
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MM-numbers of sets of sets with no singletons are A329630.
The case without empty edges is A329554.
MM-numbers of sets of sets are A302494.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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