%I #8 Feb 07 2021 06:25:54

%S 4,9,16,24,25,36,40,49,54,56,64,81,88,96,100,104,121,135,136,144,152,

%T 160,169,184,189,196,216,224,225,232,240,248,250,256,289,296,297,324,

%U 328,336,344,351,352,360,361,375,376,384,400,416,424,441,459,472,484

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

%C A squarefree semiprime (A006881) is a product of any two distinct primes.

%H Amiram Eldar, <a href="/A320894/b320894.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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]&]}]];

%t Select[Range[100],And[EvenQ[PrimeOmega[#]],strsqfsemfacs[#]=={}]&]

%Y Cf. A001055, A001358, A005117, A006881, A007717, A028260, A318871, A318953, A320655, A320656, A320891, A320892, A320893.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 23 2018