login
a(n) = a(n-1) + (sum of the terms, from among the first (n-1) terms of the sequence, which are coprime to the n-th Fibonacci number).
1

%I #10 Mar 02 2019 20:50:58

%S 1,2,3,6,18,22,74,173,350,627,1903,3980,11139,29437,72720,108312,

%T 337079,379735,988163,1354929,4458118,12200929,32148649,78234718,

%U 208109020,546549127,1108402372,3055896646,8105184898,8151267237,29457007624

%N a(n) = a(n-1) + (sum of the terms, from among the first (n-1) terms of the sequence, which are coprime to the n-th Fibonacci number).

%e The 6th Fibonacci number is 8. Of the first 5 terms, only terms a(1)=1 and a(3)=3 are coprime to 8. So a(6) = a(5) + 1 + 3 = 22.

%p with(combinat): a[1] := 1: for n from 2 to 30 do s := 0: for j to n-1 do if gcd(a[j], fibonacci(n)) = 1 then s := s+a[j] else s := s end if end do: a[n] := a[n-1]+s end do: seq(a[n], n = 1 .. 30); # _Emeric Deutsch_, Jul 17 2007

%Y Cf. A131787.

%K nonn

%O 1,2

%A _Leroy Quet_, Jul 15 2007

%E More terms from _Emeric Deutsch_ and _Joshua Zucker_, Jul 17 2007