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A339889
Products of distinct primes or semiprimes.
3
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, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70
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.
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.
A001358 lists semiprimes, with squarefree case A006881.
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.
Sequence in context: A369939 A178210 A013938 * A377021 A023809 A046100
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 23 2020
STATUS
approved