A216893 Fibonacci numbers whose sum of prime divisors equals two times a Fibonacci number.

1, 2, 8, 21, 55, 377, 610, 17711, 121393, 832040, 5702887, 19740274219868223167

Offset

1,2

Comments

Fibonacci number F such that sopf(F)= 2*F' where F' is a Fibonacci number and sopf(F) is the sum of the distinct primes dividing F (A008472).

a(13) > Fibonacci(1422), if it exists. - Amiram Eldar, Aug 08 2024

Links

Table of n, a(n) for n=1..12.

Example

121393 = F(26) = 233*521 is in the sequence because 233 + 521 = 2*377 = 2*F(14).

Maple

with(combinat, fibonacci):with(numtheory): for n from 2 to 300 do:x:=fibonacci(n):y:=factorset(x):n1:=nops(y): s:=sum('y[i] ', 'i'=1..n1): ii:=0:for m from 0 to n while(ii=0) do:if s =2*fibonacci(m) then ii:=1:printf(`%d, `, x): else fi:od:od:

Mathematica

fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; Select[Fibonacci[Range[2, 100]], fibQ[If[# == 1, 0, (Plus @@ FactorInteger[#][[;; , 1]])/2]] &] (* Amiram Eldar, Aug 08 2024 *)

Crossrefs

Cf. A000045, A008472.

Sequence in context: A303721 A109782 A237268 * A264245 A123044 A143229

Adjacent sequences: A216890 A216891 A216892 * A216894 A216895 A216896

Keyword

nonn,hard

Author

Michel Lagneau, Sep 19 2012

Extensions

a(1) = 1 inserted by Amiram Eldar, Aug 08 2024

Status

approved