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Numbers n such that sigma(n) divides Fibonacci(n).
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%I #16 Jun 11 2015 04:51:31

%S 1,96,120,240,600,672,1560,1680,2016,2160,2400,2520,2640,2976,3120,

%T 4200,4320,4560,5040,5160,5400,5520,6600,6960,7320,7680,7800,8736,

%U 9840,10080,10320,11400,12600,13800,14112,14160,16800,17400,17640,19560,19920,21600,22176

%N Numbers n such that sigma(n) divides Fibonacci(n).

%C It appears that a(n) is divisible by 24 for n > 1. - _Robert Israel_, Jun 09 2015

%H Paolo P. Lava and Robert Israel, <a href="/A258748/b258748.txt">Table of n, a(n) for n = 1..1000</a> (n = 1..150 from Paolo P. Lava)

%e Fibonacci(1) / sigma(1) = 1 / 1 = 1;

%e Fibonacci(96) / sigma(96) = 51680708854858323072 / 252 = 205082177995469536.

%p with(numtheory): with(combinat): P:=proc(q) local n;

%p for n from 1 to q do if type(fibonacci(n)/sigma(n),integer)

%p then print(n); fi; od; end: P(10^6);

%p # Alternative:

%p filter:= proc(n)

%p local s,M;

%p uses LinearAlgebra[Modular];

%p s:= numtheory:-sigma(n);

%p M:= Mod(s, Matrix([[1,1],[1,0]]),integer[]);

%p MatrixPower(s,M,n)[1,2] = 0

%p end proc:

%p 1, op(select(filter, [$2..10^5])); # _Robert Israel_, Jun 09 2015

%t Select[Range[10^4], 0==Mod[Fibonacci@# , DivisorSigma[1, #]] &] (* _Giovanni Resta_, Jun 09 2015 *)

%Y Cf. A000045, A000203.

%K nonn,easy

%O 1,2

%A _Paolo P. Lava_, Jun 09 2015