A337448 The numbers k for which Fibonacci(k) are Niven numbers.

1, 2, 3, 4, 5, 6, 8, 12, 18, 36, 54, 72, 84, 112, 120, 144, 160, 180, 198, 200, 216, 240, 243, 264, 286, 288, 299, 324, 358, 360, 468, 504, 528, 540, 576, 648, 720, 780, 816, 1008, 1020, 1044, 1200, 1248, 1260, 1500, 1602, 1824, 1872, 1917, 2160, 2184, 2760

Offset

1,2

Comments

For a(7) = 8, Fibonacci(8) = 21 and 21/digsum(21) = 7 is a prime number, so Fibonacci(8) is a Moran number (A001101). It seems that this is the only Moran number among the first 100000 Fibonacci numbers.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Example

Fibonacci(1) = 1 = A005349(1), so 1 is a term.
Fibonacci(8) = 21 = A005349(14), so 8 is a term.
Fibonacci(12) = 144 = A005349(8), so 12 is a term.
Fibonacci(18) = 2584 = A005349(514), so 18 is a term.

Mathematica

nivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; Select[Range[3000], nivenQ[Fibonacci[#]] &] (* Amiram Eldar, Sep 15 2020 *)

Prog

(Magma) niven:=func<n|n mod &+Intseq(n) eq 0>; [k:k in [1..2760]| niven(Fibonacci(k))];
(PARI) isok(k) = my(f=fibonacci(k)); (f % sumdigits(f)) == 0; \\ Michel Marcus, Sep 15 2020

Crossrefs

Cf. A000045, A004090, A001101, A005349, A117774, A337449.

Sequence in context: A143285 A346077 A335303 * A019532 A008537 A277195

Adjacent sequences: A337445 A337446 A337447 * A337449 A337450 A337451

Keyword

nonn,base

Author

Marius A. Burtea, Sep 14 2020

Status

approved