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A329554 Smallest MM-number of a set of n nonempty sets with no singletons. 5

%I #8 Dec 05 2019 17:40:37

%S 1,13,377,16211,761917,55619941,4393975339,443791509239,

%T 50148440544007,6870336354528959,954976753279525301,

%U 142291536238649269849,23193520406899830985387,3873317907952271774559629,701070541339361191195292849,139513037726532877047863276951

%N Smallest MM-number of a set of n nonempty sets with no singletons.

%C 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}}.

%F a(n) = Product_{i = 1..n} prime(A120944(i)).

%e The sequence of terms together with their corresponding systems begins:

%e 1: {}

%e 13: {{1,2}}

%e 377: {{1,2},{1,3}}

%e 16211: {{1,2},{1,3},{1,4}}

%e 761917: {{1,2},{1,3},{1,4},{2,3}}

%t sqvs=Select[Range[2,30],SquareFreeQ[#]&&!PrimeQ[#]&];

%t Table[Times@@Prime/@Take[sqvs,k],{k,0,Length[sqvs]}]

%Y The smallest BII-number of a set of n sets is A000225(n).

%Y BII-numbers of set-systems with no singletons are A326781.

%Y MM-numbers of sets of nonempty sets are the odd terms of A302494.

%Y MM-numbers of multisets of nonempty non-singleton sets are A320629.

%Y The version with empty edges is A329556.

%Y The version with singletons is A329557.

%Y The version with empty edges and singletons is A329558.

%Y Cf. A056239, A072639, A112798, A279952, A302242, A326031, A329552, A329556.

%Y Classes of MM-numbers: A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A329559 (clutters).

%K nonn

%O 0,2

%A _Gus Wiseman_, Nov 17 2019

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)