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A216893 Fibonacci numbers whose sum of prime divisors equals two times a Fibonacci number. 1

%I #6 Sep 19 2012 18:35:42

%S 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).

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

%Y Cf. A008472, A000045

%K nonn,hard

%O 1,1

%A _Michel Lagneau_, Sep 19 2012

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