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A106740 Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n, k) = gcd(Fibonacci(n), Fibonacci(k)).

%I A106740 #11 Sep 18 2021 04:22:54
%S A106740 2,1,3,1,1,5,2,1,1,8,1,1,1,1,13,1,3,1,1,1,21,2,1,1,2,1,1,34,1,1,5,1,1,
%T A106740 1,1,55,1,1,1,1,1,1,1,1,89,2,3,1,8,1,3,2,1,1,144,1,1,1,1,1,1,1,1,1,1,
%U A106740 233,1,1,1,1,13,1,1,1,1,1,1,377,2,1,5,2,1,1,2,5,1,2,1,1,610
%N A106740 Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n, k) = gcd(Fibonacci(n), Fibonacci(k)).
%H A106740 G. C. Greubel, <a href="/A106740/b106740.txt">Rows n = 3..52 of the triangle, flattened</a>
%F A106740 T(n, k) = gcd(A000045(n), A000045(k)) for n >= 3 and 3 <= k <= n.
%F A106740 T(n, 3) = abs(A061347(n)).
%F A106740 T(n, 4) = A093148(n-1).
%F A106740 T(n, n) = A000045(n).
%F A106740 From _G. C. Greubel_, Sep 11 2021: (Start)
%F A106740 T(n, 3) = A131534(n-2).
%F A106740 T(n, 5) = A060904(n).
%F A106740 T(n, 6) = A010125(n).
%F A106740 T(n, n-1) = T(n, n-2) = A000012(n).
%F A106740 T(n, n-3) = A093148(n-5).
%F A106740 T(n, n-4) = A093148(n-5).
%F A106740 T(n, n-5) = A060904(n-5).
%F A106740 T(n, n-6) = A010125(n-6). (End)
%e A106740 Triangle begins as:
%e A106740   2;
%e A106740   1, 3;
%e A106740   1, 1, 5;
%e A106740   2, 1, 1, 8;
%e A106740   1, 1, 1, 1, 13;
%e A106740   1, 3, 1, 1,  1, 21;
%e A106740   2, 1, 1, 2,  1,  1, 34;
%e A106740   1, 1, 5, 1,  1,  1,  1, 55;
%e A106740   1, 1, 1, 1,  1,  1,  1,  1, 89;
%e A106740   2, 3, 1, 8,  1,  3,  2,  1,  1, 144;
%e A106740   1, 1, 1, 1,  1,  1,  1,  1,  1,   1, 233;
%e A106740   1, 1, 1, 1, 13,  1,  1,  1,  1,   1,   1, 377;
%e A106740   2, 1, 5, 2,  1,  1,  2,  5,  1,   2,   1,   1, 610;
%t A106740 T[n_, k_]:= GCD[Fibonacci[n], Fibonacci[k]];
%t A106740 Table[T[n, k], {n,3,18}, {k,3,n}]//Flatten (* _G. C. Greubel_, Sep 11 2021 *)
%o A106740 (Sage)
%o A106740 def T(n,k): return gcd(fibonacci(n), fibonacci(k))
%o A106740 flatten([[T(n,k) for k in (3..n)] for n in (3..18)]) # _G. C. Greubel_, Sep 11 2021
%Y A106740 Cf. A000012, A000045, A010125, A060904, A061347, A093148, A131534.
%K A106740 nonn,tabl
%O A106740 3,1
%A A106740 _Reinhard Zumkeller_, May 15 2005