A320911 Numbers with an even number of prime factors (counted with multiplicity) that can be factored into squarefree semiprimes.

1, 6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 122, 123, 126, 129, 132, 133, 134, 140, 141, 142, 143, 145, 146, 150, 155, 156, 158, 159

Offset

1,2

Comments

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

Also numbers with an even number x of prime factors, whose prime multiplicities do not exceed x/2.

Links

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

Example

360 is in the sequence because it can be factored into squarefree semiprimes as (6*6*10).
4620 is in the sequence, and can be factored into squarefree semiprimes in 6 ways: (6*10*77), (6*14*55), (6*22*35), (10*14*33), (10*21*22), (14*15*22).

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

Crossrefs

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

Sequence in context: A052053 A276818 A325259 * A371781 A362617 A238748

Adjacent sequences: A320908 A320909 A320910 * A320912 A320913 A320914

Keyword

nonn

Author

Gus Wiseman, Oct 23 2018

Status

approved