OFFSET
1,2
COMMENTS
Numbers that can be factored into distinct primes or semiprimes.
A semiprime (A001358) is a product of any two prime numbers.
LINKS
EXAMPLE
See A339840 for examples.
MAPLE
N:= 100: # for terms <= N
B:= select(t -> numtheory:-bigomega(t) <= 2, {$2..N}):
S:= {1}:
for b in B do
S:= S union map(`*`, select(`<=`, S, N/b), b)
od:
sort(convert(S, list)); # Robert Israel, Dec 28 2020
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Select[Range[100], Select[facs[#], UnsameQ@@#&&SubsetQ[{1, 2}, PrimeOmega/@#]&]!={}&]
CROSSREFS
See link for additional cross-references.
Allowing only primes gives A005117.
Not allowing squares of primes gives A339741.
Positions of nonzeros in A339839.
Complement of A339840.
A001055 counts factorizations.
A320663 counts non-isomorphic multiset partitions into singletons or pairs.
A320732 counts factorizations into primes or semiprimes.
A339742 counts factorizations into distinct primes or squarefree semiprimes.
A339841 have exactly one factorization into primes or semiprimes.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 23 2020
STATUS
approved