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A272589
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.
0
1, 2, 4, 6, 7, 12, 24
OFFSET
1,2
COMMENTS
Corresponding distinct F(n) values for listed terms are 1, 3, 8, 13, 144, 46368.
Corresponding F(i) + F(j) values are for listed terms are 1, 2, 7, 9, 94, 28678.
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.
EXAMPLE
7 is a term because Fibonacci(7) = 13 = sigma(1 + 8) and 1, 8 are Fibonacci numbers.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Altug Alkan, May 03 2016
STATUS
approved