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A320893
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).
24
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
OFFSET
1,1
COMMENTS
A semiprime (A001358) is a product of any two not necessarily distinct primes.
MATHEMATICA
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[#]!={}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved