A320893 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).

1296, 7776, 10000, 12960, 18144, 19440, 21600, 27216, 28512, 33696, 36000, 38416, 42336, 42768, 44064, 46656, 48600, 49248, 50544, 50625, 59616, 60000, 66096, 73872, 75168, 77760, 80352, 89424, 95256, 95904, 98784, 100000

Offset: 1

Author

Gus Wiseman, Oct 23 2018

Keywords

• nonn

Comments

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

Crossrefs

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

Programs

Mathematica

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]&]}]];
strsemfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strsemfacs[n/d],Min@@#>d&]],{d,Select[Rest[Divisors[n]],PrimeOmega[#]==2&]}]];
Select[Range[10000],And[EvenQ[PrimeOmega[#]],strsemfacs[#]=={},sqfsemfacs[#]!={}]&]