A329629 Products of distinct odd primes of squarefree index.

1, 3, 5, 11, 13, 15, 17, 29, 31, 33, 39, 41, 43, 47, 51, 55, 59, 65, 67, 73, 79, 83, 85, 87, 93, 101, 109, 113, 123, 127, 129, 137, 139, 141, 143, 145, 149, 155, 157, 163, 165, 167, 177, 179, 181, 187, 191, 195, 199, 201, 205, 211, 215, 219, 221, 233, 235, 237

Offset

1,2

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}}. This sequence lists all MM-numbers of set-systems (sets of nonempty sets).

Links

Table of n, a(n) for n=1..58.

Example

The sequence of terms together with their corresponding set-systems begins:
   1: {}
   3: {{1}}
   5: {{2}}
  11: {{3}}
  13: {{1,2}}
  15: {{1},{2}}
  17: {{4}}
  29: {{1,3}}
  31: {{5}}
  33: {{1},{3}}
  39: {{1},{1,2}}
  41: {{6}}
  43: {{1,4}}
  47: {{2,3}}
  51: {{1},{4}}
  55: {{2},{3}}
  59: {{7}}
  65: {{2},{1,2}}
  67: {{8}}
  73: {{2,4}}

Mathematica

Select[Range[100], OddQ[#]&&SquareFreeQ[#]&&And@@SquareFreeQ/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]&]

Crossrefs

Allowing even terms (systems with empty edges) gives A302494.

Cf. A005117, A056239, A112798, A302242, A327398, A328514, A329557, A329630.

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

Sequence in context: A130603 A069977 A284795 * A340019 A302521 A270699

Adjacent sequences: A329626 A329627 A329628 * A329630 A329631 A329632

Keyword

nonn

Author

Gus Wiseman, Nov 18 2019

Status

approved