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A322525 Numbers such that the list of exponents of their factorization is a palindromic list of primes. 0
2700, 5292, 9000, 13068, 18252, 24300, 24500, 24696, 31212, 38988, 47628, 55125, 57132, 60500, 68600, 84500, 90828, 95832, 103788, 117612, 136125, 144500, 147852, 158184, 164268, 166012, 180500, 181548, 190125, 199692, 218700, 231525, 231868, 238572, 243000, 264500, 266200, 280908, 303372, 325125 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Subsequence of A242414.
Sequence in context: A254477 A115930 A109994 * A254805 A254798 A253814
KEYWORD
nonn
AUTHOR
Pierandrea Formusa, Dec 13 2018
STATUS
approved

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Last modified April 17 18:43 EDT 2024. Contains 371765 sequences. (Running on oeis4.)