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A320912
Numbers with an even number of prime factors (counted with multiplicity) that can be factored into distinct semiprimes.
31
1, 4, 6, 9, 10, 14, 15, 21, 22, 24, 25, 26, 33, 34, 35, 36, 38, 39, 40, 46, 49, 51, 54, 55, 56, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 100, 104, 106, 111, 115, 118, 119, 121, 122, 123, 126, 129, 132, 133, 134, 135, 136, 140
OFFSET
1,2
COMMENTS
A semiprime (A001358) is a product of any two not necessarily distinct primes.
LINKS
EXAMPLE
9000 is in the sequence and can be factored in either of two ways: (4*6*15*25) or (4*9*10*25).
MATHEMATICA
strsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strsemfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], PrimeOmega[#]==2&]}]];
Select[Range[100], And[EvenQ[PrimeOmega[#]], strsemfacs[#]!={}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved