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A320911
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Numbers with an even number of prime factors (counted with multiplicity) that can be factored into squarefree semiprimes.
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49
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1, 6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 122, 123, 126, 129, 132, 133, 134, 140, 141, 142, 143, 145, 146, 150, 155, 156, 158, 159
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OFFSET
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1,2
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COMMENTS
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A squarefree semiprime (A006881) is a product of any two distinct primes.
Also numbers with an even number x of prime factors, whose prime multiplicities do not exceed x/2.
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LINKS
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EXAMPLE
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360 is in the sequence because it can be factored into squarefree semiprimes as (6*6*10).
4620 is in the sequence, and can be factored into squarefree semiprimes in 6 ways: (6*10*77), (6*14*55), (6*22*35), (10*14*33), (10*21*22), (14*15*22).
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MATHEMATICA
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sqfsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sqfsemfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]];
Select[Range[100], And[EvenQ[PrimeOmega[#]], sqfsemfacs[#]!={}]&]
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CROSSREFS
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Cf. A001055, A001222, A001358, A005117, A006881, A007717, A028260, A320655, A320656, A320891, A320892, A320893, A320894, A320912.
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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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