OFFSET
1,1
COMMENTS
A squarefree semiprime (A006881) is a product of any two distinct primes.
Also numbers with an even number x of prime factors, whose greatest prime multiplicity exceeds x/2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
A complete list of all factorizations of 24 is:
(2*2*2*3),
(2*2*6), (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.
MATHEMATICA
semfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[semfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]];
Select[Range[100], And[EvenQ[PrimeOmega[#]], semfacs[#]=={}]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved