A076518 Numbers n such that Fibonacci(n) == sigma(n) (mod n).

1, 2, 4, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 120, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 348, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 509, 521, 541, 569, 571

Offset: 1

Author

Joseph L. Pe, Oct 17 2002

Keywords

• nonn

Comments

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.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

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

PARI

fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
is(n)=fibmod(n,n)==sigma(n) \\ Charles R Greathouse IV, Nov 27 2016