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A322525 Numbers such that the list of exponents of their factorization is a palindromic list of primes.

%I A322525 #25 Jan 27 2019 09:02:09
%S A322525 2700,5292,9000,13068,18252,24300,24500,24696,31212,38988,47628,55125,
%T A322525 57132,60500,68600,84500,90828,95832,103788,117612,136125,144500,
%U A322525 147852,158184,164268,166012,180500,181548,190125,199692,218700,231525,231868,238572,243000,264500,266200,280908,303372,325125
%N A322525 Numbers such that the list of exponents of their factorization is a palindromic list of primes.
%C A322525 I mean nontrivial palindrome: more than one number and not all equal numbers.
%C A322525 Factorization is meant to produce p1^e1*...*pk^ek, with pi in increasing order.
%e A322525 9000 is a term as 9000=2^3*3^2*5^3 and the correspondent exponents list [3,2,3] is a palindromic list of primes.
%t A322525 aQ[s_] := Length[Union[s]]>1 && AllTrue[s, PrimeQ] && PalindromeQ[s]; Select[Range[1000], aQ[FactorInteger[#][[;;,2]]] &] (* _Amiram Eldar_, Dec 14 2018 *)
%o A322525 (Python)
%o A322525 from sympy.ntheory import factorint,isprime
%o A322525 def all_prime(l):
%o A322525     for i in l:
%o A322525         if not(isprime(i)): return(False)
%o A322525     return(True)
%o A322525 def all_equal(l):
%o A322525     ll=len(l)
%o A322525     set_l=set(l)
%o A322525     lsl=list(set_l)
%o A322525     llsl=len(lsl)
%o A322525     return(llsl==1)
%o A322525 def pal(l):
%o A322525     return(l == l[::-1])
%o A322525 n=350000
%o A322525 r=""
%o A322525 lp=[]
%o A322525 lexp=[]
%o A322525 def calc(n):
%o A322525     global lp,lexp
%o A322525     a=factorint(n)
%o A322525     lp=[]
%o A322525     for p in a.keys():
%o A322525         lp.append(p)
%o A322525     lexp=[]
%o A322525     for exp in a.values():
%o A322525         lexp.append(exp)
%o A322525     return
%o A322525 for i in range(4,n):
%o A322525     calc(i)
%o A322525     if len(lexp)>1:
%o A322525         if all_prime(lexp):
%o A322525             if not(all_equal(lexp)):
%o A322525                 if pal(lexp):
%o A322525                     r += ","+str(i)
%o A322525 print(r[1:])
%o A322525 (PARI) isok(n) = (ve=factor(n)[,2]~) && (Vecrev(ve)==ve) && (#ve>1) && (#Set(ve)>1) && (#select(x->(!isprime(x)), ve) == 0); \\ _Michel Marcus_, Dec 14 2018
%Y A322525 Subsequence of A242414.
%K A322525 nonn
%O A322525 1,1
%A A322525 _Pierandrea Formusa_, Dec 13 2018