login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
Sequence in context: A175116 A153484 A060660 * A323629 A146992 A261287
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Jun 09 2015
STATUS
approved