|
%I #18 May 05 2016 21:23:56
%S 1,2,4,6,7,12,24
%N Numbers n such that the equation F(n) = sigma(F(i) + F(j)) has a solution with i >= 1 and j >= 0, where F(k) = A000045(k) represents the k-th Fibonacci number.
%C Corresponding distinct F(n) values for listed terms are 1, 3, 8, 13, 144, 46368.
%C Corresponding F(i) + F(j) values are for listed terms are 1, 2, 7, 9, 94, 28678.
%C It is known that for almost all positive integers n, the sum of divisors of Fibonacci(n) is not a Fibonacci number (see A272412). This sequence focuses on the sums of two Fibonacci numbers for a similar question. Since A000045 is obvious subsequence of A084176 by definition of Fibonacci numbers, the reason of existence of this sequence can be seen as a generalized version of question that is motivation of A272412.
%e 7 is a term because Fibonacci(7) = 13 = sigma(1 + 8) and 1, 8 are Fibonacci numbers.
%Y Cf. A000203, A000045, A084176, A272412.
%K nonn,more
%O 1,2
%A _Altug Alkan_, May 03 2016
|
