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A329558 Product of primes indexed by the first n squarefree numbers.

%I A329558 #15 Feb 24 2020 06:04:20
%S A329558 1,2,6,30,330,4290,72930,2114970,65564070,2688126870,115589455410,
%T A329558 5432704404270,320529559851930,21475480510079310,1567710077235789630,
%U A329558 123849096101627380770,10279474976435072603910,1038226972619942332994910,113166740015573714296445190,12787841621759829715498306470
%N A329558 Product of primes indexed by the first n squarefree numbers.
%C A329558 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}}. Then a(n) is the smallest MM-number of a set of n sets.
%H A329558 Jinyuan Wang, <a href="/A329558/b329558.txt">Table of n, a(n) for n = 0..100</a>
%F A329558 a(n > 0) = 2 * A329557(n - 1).
%F A329558 a(n) = Product_{i = 1..n} prime(A005117(i)).
%e A329558 The sequence of terms together with their corresponding systems begins:
%e A329558         1: {}
%e A329558         2: {{}}
%e A329558         6: {{},{1}}
%e A329558        30: {{},{1},{2}}
%e A329558       330: {{},{1},{2},{3}}
%e A329558      4290: {{},{1},{2},{3},{1,2}}
%e A329558     72930: {{},{1},{2},{3},{1,2},{4}}
%e A329558   2114970: {{},{1},{2},{3},{1,2},{4},{1,3}}
%t A329558 sqvs=Select[Range[30],SquareFreeQ];
%t A329558 Table[Times@@Prime/@Take[sqvs,k],{k,0,Length[sqvs]}]
%Y A329558 The smallest BII-number of a set of n sets is A000225(n).
%Y A329558 MM-numbers of sets of sets are A302494.
%Y A329558 The case without empty edges is A329557.
%Y A329558 The case without singletons is A329556.
%Y A329558 The case without empty edges or singletons is A329554.
%Y A329558 The connected version is A329552.
%Y A329558 Cf. A005117, A048672, A056239, A072639, A112798, A302242, A326031, A329555.
%Y A329558 Classes of MM-numbers: A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A329559 (clutters).
%K A329558 nonn
%O A329558 0,2
%A A329558 _Gus Wiseman_, Nov 17 2019
%E A329558 a(19) from _Jinyuan Wang_, Feb 24 2020