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A258748
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Numbers n such that sigma(n) divides Fibonacci(n).
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2
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1, 96, 120, 240, 600, 672, 1560, 1680, 2016, 2160, 2400, 2520, 2640, 2976, 3120, 4200, 4320, 4560, 5040, 5160, 5400, 5520, 6600, 6960, 7320, 7680, 7800, 8736, 9840, 10080, 10320, 11400, 12600, 13800, 14112, 14160, 16800, 17400, 17640, 19560, 19920, 21600, 22176
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OFFSET
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1,2
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COMMENTS
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It appears that a(n) is divisible by 24 for n > 1. - Robert Israel, Jun 09 2015
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LINKS
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EXAMPLE
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Fibonacci(1) / sigma(1) = 1 / 1 = 1;
Fibonacci(96) / sigma(96) = 51680708854858323072 / 252 = 205082177995469536.
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MAPLE
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with(numtheory): with(combinat): P:=proc(q) local n;
for n from 1 to q do if type(fibonacci(n)/sigma(n), integer)
then print(n); fi; od; end: P(10^6);
# Alternative:
filter:= proc(n)
local s, M;
uses LinearAlgebra[Modular];
s:= numtheory:-sigma(n);
M:= Mod(s, Matrix([[1, 1], [1, 0]]), integer[]);
MatrixPower(s, M, n)[1, 2] = 0
end proc:
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MATHEMATICA
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Select[Range[10^4], 0==Mod[Fibonacci@# , DivisorSigma[1, #]] &] (* Giovanni Resta, Jun 09 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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