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A339889
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Products of distinct primes or semiprimes.
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3
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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
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OFFSET
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1,2
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COMMENTS
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Numbers that can be factored into distinct primes or semiprimes.
A semiprime (A001358) is a product of any two prime numbers.
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LINKS
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EXAMPLE
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MAPLE
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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:
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MATHEMATICA
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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/@#]&]!={}&]
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CROSSREFS
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See link for additional cross-references.
Allowing only primes gives A005117.
Not allowing squares of primes gives A339741.
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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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