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A329554
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Smallest MM-number of a set of n nonempty sets with no singletons.
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5
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1, 13, 377, 16211, 761917, 55619941, 4393975339, 443791509239, 50148440544007, 6870336354528959, 954976753279525301, 142291536238649269849, 23193520406899830985387, 3873317907952271774559629, 701070541339361191195292849, 139513037726532877047863276951
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OFFSET
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0,2
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COMMENTS
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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}}.
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LINKS
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FORMULA
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a(n) = Product_{i = 1..n} prime(A120944(i)).
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EXAMPLE
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The sequence of terms together with their corresponding systems begins:
1: {}
13: {{1,2}}
377: {{1,2},{1,3}}
16211: {{1,2},{1,3},{1,4}}
761917: {{1,2},{1,3},{1,4},{2,3}}
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MATHEMATICA
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sqvs=Select[Range[2, 30], SquareFreeQ[#]&&!PrimeQ[#]&];
Table[Times@@Prime/@Take[sqvs, k], {k, 0, Length[sqvs]}]
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CROSSREFS
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The smallest BII-number of a set of n sets is A000225(n).
BII-numbers of set-systems with no singletons are A326781.
MM-numbers of sets of nonempty sets are the odd terms of A302494.
MM-numbers of multisets of nonempty non-singleton sets are A320629.
The version with empty edges is A329556.
The version with singletons is A329557.
The version with empty edges and singletons is A329558.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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