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A258748 Numbers n such that sigma(n) divides Fibonacci(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that a(n) is divisible by 24 for n > 1. - Robert Israel, Jun 09 2015

LINKS

Paolo P. Lava and Robert Israel, Table of n, a(n) for n = 1..1000 (n = 1..150 from Paolo P. Lava)

EXAMPLE

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

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

MAPLE

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:

1, op(select(filter, [$2..10^5])); # Robert Israel, Jun 09 2015

MATHEMATICA

Select[Range[10^4], 0==Mod[Fibonacci@# , DivisorSigma[1, #]] &] (* Giovanni Resta, Jun 09 2015 *)

CROSSREFS

Cf. A000045, A000203.

Sequence in context: A175116 A153484 A060660 * A323629 A146992 A261287

Adjacent sequences:  A258745 A258746 A258747 * A258749 A258750 A258751

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, Jun 09 2015

STATUS

approved

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Last modified June 6 11:14 EDT 2020. Contains 334827 sequences. (Running on oeis4.)