cp's OEIS Frontend

A339889 Products of distinct primes or semiprimes.

%I A339889 #19 Jan 08 2021 20:36:31
%S A339889 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,
%T A339889 28,29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A339889 52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70
%N A339889 Products of distinct primes or semiprimes.
%C A339889 Numbers that can be factored into distinct primes or semiprimes.
%C A339889 A semiprime (A001358) is a product of any two prime numbers.
%H A339889 Robert Israel, <a href="/A339889/b339889.txt">Table of n, a(n) for n = 1..10000</a>
%H A339889 Gus Wiseman, <a href="/A339741/a339741_1.txt">Counting and ranking factorizations, factorability, and vertex-degree partitions for groupings into pairs.</a>
%e A339889 See A339840 for examples.
%p A339889 N:= 100: # for terms <= N
%p A339889 B:= select(t -> numtheory:-bigomega(t) <= 2, {$2..N}):
%p A339889 S:= {1}:
%p A339889 for b in B do
%p A339889   S:= S union map(`*`,select(`<=`,S,N/b),b)
%p A339889 od:
%p A339889 sort(convert(S,list)); # _Robert Israel_, Dec 28 2020
%t A339889 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A339889 Select[Range[100],Select[facs[#],UnsameQ@@#&&SubsetQ[{1,2},PrimeOmega/@#]&]!={}&]
%Y A339889 See link for additional cross-references.
%Y A339889 Allowing only primes gives A005117.
%Y A339889 Not allowing squares of primes gives A339741.
%Y A339889 Positions of nonzeros in A339839.
%Y A339889 Complement of A339840.
%Y A339889 A001055 counts factorizations.
%Y A339889 A001358 lists semiprimes, with squarefree case A006881.
%Y A339889 A320663 counts non-isomorphic multiset partitions into singletons or pairs.
%Y A339889 A320732 counts factorizations into primes or semiprimes.
%Y A339889 A339742 counts factorizations into distinct primes or squarefree semiprimes.
%Y A339889 A339841 have exactly one factorization into primes or semiprimes.
%Y A339889 Cf. A002100, A013929, A293511, A320893, A339740, A339846.
%K A339889 nonn
%O A339889 1,2
%A A339889 _Gus Wiseman_, Dec 23 2020