A320893 - OEIS

%I #7 Oct 24 2018 09:49:50

%S 1296,7776,10000,12960,18144,19440,21600,27216,28512,33696,36000,

%T 38416,42336,42768,44064,46656,48600,49248,50544,50625,59616,60000,

%U 66096,73872,75168,77760,80352,89424,95256,95904,98784,100000

%N 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).

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

%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[10000],And[EvenQ[PrimeOmega[#]],strsemfacs[#]=={},sqfsemfacs[#]!={}]&]

%Y Cf. A001055, A001358, A005117, A006881, A007717, A028260, A318871, A318953, A320655, A320656, A320891, A320892, A320894, A320911, A320912, A320913.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 23 2018