A320912 Numbers with an even number of prime factors (counted with multiplicity) that can be factored into distinct semiprimes.

1, 4, 6, 9, 10, 14, 15, 21, 22, 24, 25, 26, 33, 34, 35, 36, 38, 39, 40, 46, 49, 51, 54, 55, 56, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 100, 104, 106, 111, 115, 118, 119, 121, 122, 123, 126, 129, 132, 133, 134, 135, 136, 140

Offset: 1

Author

Gus Wiseman, Oct 23 2018

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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