A320913 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into squarefree semiprimes (A320891) but can be factored into distinct semiprimes (A320912).

4, 9, 24, 25, 40, 49, 54, 56, 88, 104, 121, 135, 136, 152, 169, 184, 189, 232, 240, 248, 250, 289, 296, 297, 328, 336, 344, 351, 361, 375, 376, 424, 459, 472, 488, 513, 528, 529, 536, 560, 568, 584, 621, 624, 632, 664, 686, 712, 776, 783, 808, 810, 816, 824

Offset: 1

Author

Gus Wiseman, Oct 23 2018

Keywords

• nonn

Comments

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

If A025487(k) is contained in this sequence then so is every positive integer with its prime signature. - David A. Corneth, Oct 24 2018

Crossrefs

Cf. A001055, A001222, A001358, A005117, A006881, A007717, A025487, A028260, A320655, A320656, A320891, A320892, A320893, A320894, A320911, A320912.

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[1000],And[EvenQ[PrimeOmega[#]],strsemfacs[#]!={},sqfsemfacs[#]=={}]&]