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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

Table of n, a(n) for n=1..40.

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

Adjacent sequences:  A322522 A322523 A322524 * A322526 A322527 A322528

KEYWORD

nonn

AUTHOR

Pierandrea Formusa, Dec 13 2018

STATUS

approved

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Last modified April 7 10:46 EDT 2020. Contains 333301 sequences. (Running on oeis4.)