OFFSET
1,2
COMMENTS
Konyagin, Luca & Stanica proved that for almost all positive integers n, the sum of the divisors of Fibonacci(n) is not a Fibonacci number (see page 7).
If the sum of the k-th powers of the divisors of Fibonacci(n) is a Fibonacci number for k > 1, then the corresponding Fibonacci(n) is 1 or 2.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems
Sergei V. Konyagin, Florian Luca and Pantelimon Stanica, Sum Of Divisors Of Fibonacci Numbers, Uniform Distribution Theory 4 (2009), no.1, 1-8.
N. J. A. Sloane, The OEIS, Mathematical Discovery, and Insomnia, Slides of plenary talk presented at Computational Discovery in Mathematics, Western University, London, Ontario, May 12-16. Mentions this sequence at page 32.
MATHEMATICA
f = Fibonacci@Range[2, 40]; Select[Range[10^6], MemberQ[f, DivisorSigma[1, #]] &] (* Giovanni Resta, Apr 29 2016 *)
PROG
(PARI) lista(nn) = for(n=1, nn, if(issquare(5*sigma(n)^2+4) || issquare(5*sigma(n)^2-4), print1(n, ", ")));
(PARI) isFibonacci(n)=my(k=n^2); issquare(k+=(k+1)<<2) || (n>0 && issquare(k-8))
is(n)=isFibonacci(sigma(n)) \\ Charles R Greathouse IV, Apr 29 2016
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Altug Alkan, Apr 29 2016
STATUS
approved