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A320894
Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into distinct squarefree semiprimes.
28
4, 9, 16, 24, 25, 36, 40, 49, 54, 56, 64, 81, 88, 96, 100, 104, 121, 135, 136, 144, 152, 160, 169, 184, 189, 196, 216, 224, 225, 232, 240, 248, 250, 256, 289, 296, 297, 324, 328, 336, 344, 351, 352, 360, 361, 375, 376, 384, 400, 416, 424, 441, 459, 472, 484
OFFSET
1,1
COMMENTS
A squarefree semiprime (A006881) is a product of any two distinct primes.
LINKS
EXAMPLE
A complete list of all strict factorizations of 24 is: (2*3*4), (2*12), (3*8), (4*6), (24). All of these contain at least one number that is not a squarefree semiprime, so 24 belongs to the sequence.
MATHEMATICA
strsqfsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strsqfsemfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]];
Select[Range[100], And[EvenQ[PrimeOmega[#]], strsqfsemfacs[#]=={}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved