A320894 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into distinct squarefree semiprimes.

4, 9, 16, 24, 25, 36, 40, 49, 54, 56, 64, 81, 88, 96, 100, 104, 121, 135, 136, 144, 152, 160, 169, 184, 189, 196, 216, 224, 225, 232, 240, 248, 250, 256, 289, 296, 297, 324, 328, 336, 344, 351, 352, 360, 361, 375, 376, 384, 400, 416, 424, 441, 459, 472, 484

Offset: 1

Author

Gus Wiseman, Oct 23 2018

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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