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

Author

Marius A. Burtea, Sep 14 2020

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Magma

niven:=func; [k:k in [1..2760]| niven(Fibonacci(k))];

Mathematica

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

PARI

isok(k) = my(f=fibonacci(k)); (f % sumdigits(f)) == 0; \\ Michel Marcus, Sep 15 2020