[seqfan] Palindromes over prime factorization

Vladimir Shevelev shevelev at bgu.ac.il
Sat Dec 12 15:59:31 CET 2015

Dear SeqFans,

In A265640 I introduced so-called "Palindromes 
over prime factorization". A number N is called a
prime factorization palindrome (PFP) if all its 
prime factors, taking into account their multiplicities,
can be ordered on a line centrally symmetric.
Examples: 44=2*11*2, 180=2*3*5*3*2.
This type of "palindromes" does not depend on base.
It is easy to see that every PFP-number >1 is either
a square or a product of a square >=1 and a prime.
 In particular, the sequence contains all primes. 
Therefore, if A(x) is the number of PFP <= x, then 
lim A(x)/pi(x) = zeta(2), where {pi(n)} = A000720.
See also A265641.
All remarks are welcome. 

Best regards,


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