OFFSET
1,1
COMMENTS
I mean nontrivial palindrome: more than one number and not all equal numbers.
Factorization is meant to produce p1^e1*...*pk^ek, with pi in increasing order.
EXAMPLE
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.
MATHEMATICA
aQ[s_] := Length[Union[s]]>1 && AllTrue[s, PrimeQ] && PalindromeQ[s]; Select[Range[1000], aQ[FactorInteger[#][[;; , 2]]] &] (* Amiram Eldar, Dec 14 2018 *)
PROG
(Python)
from sympy.ntheory import factorint, isprime
def all_prime(l):
for i in l:
if not(isprime(i)): return(False)
return(True)
def all_equal(l):
ll=len(l)
set_l=set(l)
lsl=list(set_l)
llsl=len(lsl)
return(llsl==1)
def pal(l):
return(l == l[::-1])
n=350000
r=""
lp=[]
lexp=[]
def calc(n):
global lp, lexp
a=factorint(n)
lp=[]
for p in a.keys():
lp.append(p)
lexp=[]
for exp in a.values():
lexp.append(exp)
return
for i in range(4, n):
calc(i)
if len(lexp)>1:
if all_prime(lexp):
if not(all_equal(lexp)):
if pal(lexp):
r += ", "+str(i)
print(r[1:])
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Pierandrea Formusa, Dec 13 2018
STATUS
approved