OFFSET
1,1
COMMENTS
Obviously the least prime factor of a composite number k can't be greater than sqrt(k). However, it can be greater than some function that grows more slowly than sqrt(k); k^(1/(log log k)^2) is just one possibility.
LINKS
Encyclopedia of Mathematics, Quasi-prime number
EXAMPLE
539 = 7^2 * 11, and 539^(1/(log log 539)^2) = 6.42358133145183..., which is less than least prime factor 7. Hence 539 is in the sequence.
540 = 2^2 * 3^3 * 5, and 540^(1/(log log 540)^2 = 6.423273267433689..., which is greater than least prime factor 2, so 540 is not in the sequence.
MATHEMATICA
Select[Range[1000], Not[PrimeQ[#]] && FactorInteger[#][[1, 1]] > #^(1/Log[Log[#]]^2) &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Alonso del Arte, Oct 01 2018
STATUS
approved