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%I #15 Aug 08 2024 06:41:27
%S 1,2,8,21,55,377,610,17711,121393,832040,5702887,19740274219868223167
%N Fibonacci numbers whose sum of prime divisors equals two times a Fibonacci number.
%C 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).
%C a(13) > Fibonacci(1422), if it exists. - _Amiram Eldar_, Aug 08 2024
%e 121393 = F(26) = 233*521 is in the sequence because 233 + 521 = 2*377 = 2*F(14).
%p 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:
%t 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 *)
%Y Cf. A000045, A008472.
%K nonn,hard
%O 1,2
%A _Michel Lagneau_, Sep 19 2012
%E a(1) = 1 inserted by _Amiram Eldar_, Aug 08 2024
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