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%I #10 Mar 02 2019 23:31:44
%S 1,2,3,5,8,11,17,23,28,35,45,51,63,76,83,92,108,117,135,144,156,177,
%T 199,205,224,249,264,279,307,319,349,364,385,418,443,456,492,529,553,
%U 566,606,629,671,696,713,758,804,817,862,899,929,962,1014,1041,1089,1114
%N a(n) = a(n-1) + (number of 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, a(3)=3 and a(4) = 5 are coprime to 8. Since there are 3 such terms, a(6) = a(5) + 3 = 11.
%p with(combinat): a[1]:= 1: for n from 2 to 55 do ct := 0: for j to n-1 do if gcd(a[j], fibonacci(n)) = 1 then ct := ct+1 else ct := ct end if end do: a[n]:= a[n-1]+ct end do: seq(a[n], n = 1 .. 55); # _Emeric Deutsch_, Jul 24 2007
%Y Cf. A131788.
%K nonn
%O 1,2
%A _Leroy Quet_, Jul 15 2007
%E More terms from _Joshua Zucker_ and _Emeric Deutsch_, Jul 18 2007