cp's OEIS Frontend

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

%I A329554 #8 Dec 05 2019 17:40:37
%S A329554 1,13,377,16211,761917,55619941,4393975339,443791509239,
%T A329554 50148440544007,6870336354528959,954976753279525301,
%U A329554 142291536238649269849,23193520406899830985387,3873317907952271774559629,701070541339361191195292849,139513037726532877047863276951
%N A329554 Smallest MM-number of a set of n nonempty sets with no singletons.
%C A329554 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 A329554 a(n) = Product_{i = 1..n} prime(A120944(i)).
%e A329554 The sequence of terms together with their corresponding systems begins:
%e A329554        1: {}
%e A329554       13: {{1,2}}
%e A329554      377: {{1,2},{1,3}}
%e A329554    16211: {{1,2},{1,3},{1,4}}
%e A329554   761917: {{1,2},{1,3},{1,4},{2,3}}
%t A329554 sqvs=Select[Range[2,30],SquareFreeQ[#]&&!PrimeQ[#]&];
%t A329554 Table[Times@@Prime/@Take[sqvs,k],{k,0,Length[sqvs]}]
%Y A329554 The smallest BII-number of a set of n sets is A000225(n).
%Y A329554 BII-numbers of set-systems with no singletons are A326781.
%Y A329554 MM-numbers of sets of nonempty sets are the odd terms of A302494.
%Y A329554 MM-numbers of multisets of nonempty non-singleton sets are A320629.
%Y A329554 The version with empty edges is A329556.
%Y A329554 The version with singletons is A329557.
%Y A329554 The version with empty edges and singletons is A329558.
%Y A329554 Cf. A056239, A072639, A112798, A279952, A302242, A326031, A329552, A329556.
%Y A329554 Classes of MM-numbers: A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A329559 (clutters).
%K A329554 nonn
%O A329554 0,2
%A A329554 _Gus Wiseman_, Nov 17 2019