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A373116
Fibonacci numbers whose digits product is a positive perfect power (A001597).
1
1, 8, 55, 144, 4181, 17711, 196418, 1346269, 259695496911122585
OFFSET
1,2
COMMENTS
Since the product of the digits of Fibonacci(k) is required to be positive, Fibonacci(k) does not have zero as a digit. For this reason this list is probably finite, since it is conjectured that there are only finitely many Fibonacci numbers that do not contain the digit zero (see A076564). If the conjecture is true, the largest number possessing the property would be Fibonacci(85) = 259695496911122585 whose digit product is 194400^2.
Unlike A373049, here the product uses all the digits of Fibonacci(k).
EXAMPLE
196418 is a term, because Fibonacci(27) = 196418 and the product of its digits is 1*9*6*4*1*8 = 12^3.
MATHEMATICA
powQ[n_] := n == 1 || GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Fibonacci[Range[2, 100]], powQ[Times @@ IntegerDigits[#]] &] (* Amiram Eldar, May 25 2024 *)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Gonzalo Martínez, May 25 2024
STATUS
approved