A258748 Numbers n such that sigma(n) divides Fibonacci(n).

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

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