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