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

1, 2, 6, 30, 330, 4290, 72930, 2114970, 65564070, 2688126870, 115589455410, 5432704404270, 320529559851930, 21475480510079310, 1567710077235789630, 123849096101627380770, 10279474976435072603910, 1038226972619942332994910, 113166740015573714296445190, 12787841621759829715498306470

Offset

0,2

Comments

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.

Links

Jinyuan Wang, Table of n, a(n) for n = 0..100

Formula

a(n > 0) = 2 * A329557(n - 1).

a(n) = Product_{i = 1..n} prime(A005117(i)).

Example

The sequence of terms together with their corresponding systems begins:
        1: {}
        2: {{}}
        6: {{},{1}}
       30: {{},{1},{2}}
      330: {{},{1},{2},{3}}
     4290: {{},{1},{2},{3},{1,2}}
    72930: {{},{1},{2},{3},{1,2},{4}}
  2114970: {{},{1},{2},{3},{1,2},{4},{1,3}}

Mathematica

sqvs=Select[Range[30], SquareFreeQ];
Table[Times@@Prime/@Take[sqvs, k], {k, 0, Length[sqvs]}]

Crossrefs

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

MM-numbers of sets of sets are A302494.

The case without empty edges is A329557.

The case without singletons is A329556.

The case without empty edges or singletons is A329554.

The connected version is A329552.

Cf. A005117, A048672, A056239, A072639, A112798, A302242, A326031, A329555.

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

Sequence in context: A120295 A071350 A324853 * A038696 A333373 A064847

Adjacent sequences: A329555 A329556 A329557 * A329559 A329560 A329561

Keyword

nonn

Author

Gus Wiseman, Nov 17 2019

Extensions

a(19) from Jinyuan Wang, Feb 24 2020

Status

approved