A373116 Fibonacci numbers whose digits product is a positive perfect power (A001597).

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).

Links

Table of n, a(n) for n=1..9.

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

Cf. A000045, A001597, A076564, A246558, A370071, A373049.

Sequence in context: A080312 A116885 A179407 * A244501 A026994 A110184

Adjacent sequences: A373113 A373114 A373115 * A373117 A373118 A373119

Keyword

nonn,base,more

Author

Gonzalo Martínez, May 25 2024

Status

approved