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Numbers with an even number of prime factors (counted with multiplicity) that can be factored into distinct semiprimes.
31

%I #9 Feb 07 2021 06:26:10

%S 1,4,6,9,10,14,15,21,22,24,25,26,33,34,35,36,38,39,40,46,49,51,54,55,

%T 56,57,58,60,62,65,69,74,77,82,84,85,86,87,88,90,91,93,94,95,100,104,

%U 106,111,115,118,119,121,122,123,126,129,132,133,134,135,136,140

%N Numbers with an even number of prime factors (counted with multiplicity) that can be factored into distinct semiprimes.

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

%H Amiram Eldar, <a href="/A320912/b320912.txt">Table of n, a(n) for n = 1..10000</a>

%e 9000 is in the sequence and can be factored in either of two ways: (4*6*15*25) or (4*9*10*25).

%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[100],And[EvenQ[PrimeOmega[#]],strsemfacs[#]!={}]&]

%Y Cf. A001055, A001222, A001358, A007717, A028260, A320655, A320892, A320893, A320894, A320911.

%K nonn

%O 1,2

%A _Gus Wiseman_, Oct 23 2018