cp's OEIS Frontend

A329629 Products of distinct odd primes of squarefree index.

%I A329629 #6 Nov 18 2019 23:15:28
%S A329629 1,3,5,11,13,15,17,29,31,33,39,41,43,47,51,55,59,65,67,73,79,83,85,87,
%T A329629 93,101,109,113,123,127,129,137,139,141,143,145,149,155,157,163,165,
%U A329629 167,177,179,181,187,191,195,199,201,205,211,215,219,221,233,235,237
%N A329629 Products of distinct odd primes of squarefree index.
%C A329629 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).
%e A329629 The sequence of terms together with their corresponding set-systems begins:
%e A329629    1: {}
%e A329629    3: {{1}}
%e A329629    5: {{2}}
%e A329629   11: {{3}}
%e A329629   13: {{1,2}}
%e A329629   15: {{1},{2}}
%e A329629   17: {{4}}
%e A329629   29: {{1,3}}
%e A329629   31: {{5}}
%e A329629   33: {{1},{3}}
%e A329629   39: {{1},{1,2}}
%e A329629   41: {{6}}
%e A329629   43: {{1,4}}
%e A329629   47: {{2,3}}
%e A329629   51: {{1},{4}}
%e A329629   55: {{2},{3}}
%e A329629   59: {{7}}
%e A329629   65: {{2},{1,2}}
%e A329629   67: {{8}}
%e A329629   73: {{2,4}}
%t A329629 Select[Range[100],OddQ[#]&&SquareFreeQ[#]&&And@@SquareFreeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]
%Y A329629 Allowing even terms (systems with empty edges) gives A302494.
%Y A329629 Cf. A005117, A056239, A112798, A302242, A327398, A328514, A329557, A329630.
%Y A329629 Classes of MM-numbers: A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A329559 (clutters).
%K A329629 nonn
%O A329629 1,2
%A A329629 _Gus Wiseman_, Nov 18 2019