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A320893
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Numbers with an even number of prime factors (counted with multiplicity) that can be factored into squarefree semiprimes (A320911) but cannot be factored into distinct semiprimes (A320892).
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24
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1296, 7776, 10000, 12960, 18144, 19440, 21600, 27216, 28512, 33696, 36000, 38416, 42336, 42768, 44064, 46656, 48600, 49248, 50544, 50625, 59616, 60000, 66096, 73872, 75168, 77760, 80352, 89424, 95256, 95904, 98784, 100000
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OFFSET
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1,1
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COMMENTS
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A semiprime (A001358) is a product of any two not necessarily distinct primes.
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LINKS
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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]&]}]];
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[10000], And[EvenQ[PrimeOmega[#]], strsemfacs[#]=={}, sqfsemfacs[#]!={}]&]
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CROSSREFS
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Cf. A001055, A001358, A005117, A006881, A007717, A028260, A318871, A318953, A320655, A320656, A320891, A320892, A320894, A320911, A320912, A320913.
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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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