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

1,2

Comments

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

Links

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

Example

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

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[#]!={}]&]

Crossrefs

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

Sequence in context: A219786 A302038 A063762 * A359765 A240938 A001358

Adjacent sequences: A320909 A320910 A320911 * A320913 A320914 A320915

Keyword

nonn

Author

Gus Wiseman, Oct 23 2018

Status

approved