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Numbers n such that Fibonacci(n) == sigma(n) (mod n).
2

%I #6 Nov 27 2016 02:34:07

%S 1,2,4,11,19,29,31,41,59,61,71,79,89,101,109,120,131,139,149,151,179,

%T 181,191,199,211,229,239,241,251,269,271,281,311,331,348,349,359,379,

%U 389,401,409,419,421,431,439,449,461,479,491,499,509,521,541,569,571

%N Numbers n such that Fibonacci(n) == sigma(n) (mod n).

%C It appears that most of the terms of this sequence satisfy Fibonacci(n) == 1 (mod n). Also it seems that most of the terms are primes.

%H Charles R Greathouse IV, <a href="/A076518/b076518.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[10^4], Mod[Fibonacci[ # ], # ] == Mod[DivisorSigma[1, # ], # ] &]

%o (PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]

%o is(n)=fibmod(n,n)==sigma(n) \\ _Charles R Greathouse IV_, Nov 27 2016

%K nonn

%O 1,2

%A _Joseph L. Pe_, Oct 17 2002