A337449 -id:A337449 - cp's OEIS frontend

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

Marius A. Burtea, Sep 14 2020

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.

			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.

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

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

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

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

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

A117789 Lucas numbers which are divisible by the sum of their digits.

Original entry on oeis.org

1, 3, 4, 7, 18, 322, 5778, 505019158607, 84722519070079276, 1473646213395791149646646123, 105249261265075663875711417309855979021650214636

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

a(12) has 83 digits and it is too large to include in the data section. - Amiram Eldar, Feb 08 2021

			322 is in the sequence because it is a Lucas number and it is divisible by the sum of its digits, 3+2+2 = 7.

Amiram Eldar, Table of n, a(n) for n = 1..17

Intersection of A000204 and A005349.

Cf. A337449.

Select[LinearRecurrence[{1, 1}, {1, 3}, 230], Divisible[#, Plus @@ IntegerDigits[#]] &] (* Amiram Eldar, Feb 08 2021 *)

{m=370;a=1;b=3;print1(a,",",b,",");for(n=3,m,c=b+a;a=b;b=c;s=0;k=b;while(k>0,d=divrem(k,10);k=d[1];s=s+d[2]);if(b%s==0,print1(b,",")))} \\ Klaus Brockhaus, Apr 17 2006

a(n) = A000204(A337449(n+1)). - Amiram Eldar, Feb 08 2021

a(9) corrected, a(10) and a(11) from Klaus Brockhaus, Apr 17 2006

cp's OEIS Frontend

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

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