%I #6 Dec 08 2018 21:03:52

%S 4,9,24,25,40,49,54,56,88,104,121,135,136,152,169,184,189,232,240,248,

%T 250,289,296,297,328,336,344,351,361,375,376,424,459,472,488,513,528,

%U 529,536,560,568,584,621,624,632,664,686,712,776,783,808,810,816,824

%N Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into squarefree semiprimes (A320891) but can be factored into distinct semiprimes (A320912).

%C A semiprime (A001358) is a product of any two not necessarily distinct primes.

%C If A025487(k) is contained in this sequence then so is every positive integer with its prime signature. - _David A. Corneth_, Oct 24 2018

%t 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]&]}]];

%t strsemfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strsemfacs[n/d],Min@@#>d&]],{d,Select[Rest[Divisors[n]],PrimeOmega[#]==2&]}]];

%t Select[Range[1000],And[EvenQ[PrimeOmega[#]],strsemfacs[#]!={},sqfsemfacs[#]=={}]&]

%Y Cf. A001055, A001222, A001358, A005117, A006881, A007717, A025487, A028260, A320655, A320656, A320891, A320892, A320893, A320894, A320911, A320912.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 23 2018