[seqfan] A266047

[Vladimir Shevelev]

Dear SeqFans,

I submitted A266047 "Smallest integers of each prime
signature of prime factorization palindromes (A265640)."
It is a subsequence of  A025487:
   1, 2, 4, 8, 12, 16, 32, 36, 48, 64, 72, 128, 144, 180, ...
Using the structure of PFP and references [Hardy and
Ramanujan], [Dusart] and [Rosser], I proved an upper
estimate for the number K(x) of a(n)<=x. It is
K(x)<=Q(sqrt(x))*(loglog(e/2*log(x*loglogx))+1.594830...+o(1)).
Here Q(x) is the number of A025487(n)<=x for which
Hardy & Ramanujan gave the known asymptotic formula.
Can anyone find an asymptotic formula for K(x),
using (or not using) function Q(x)?

Best regards,
Vladimir