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A199922 Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=3^(n-1) T(n,k) = gcd(k,3^(n-1)).

%I A199922 #12 Apr 25 2024 09:20:08
%S A199922 1,1,1,3,1,1,3,9,1,1,3,1,1,3,1,1,9,27,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,
%T A199922 1,9,1,1,3,1,1,3,1,1,27,81,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9,1,1,3,
%U A199922 1,1,3,1,1,27,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,27,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,81
%N A199922 Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=3^(n-1) T(n,k) = gcd(k,3^(n-1)).
%H A199922 G. C. Greubel, <a href="/A199922/b199922.txt">Rows n = 0..8 of the irregular triangle, flattened</a>
%F A199922 From _G. C. Greubel_, Nov 24 2023: (Start)
%F A199922 T(n, 3^(n-1) - k) = T(n, k).
%F A199922 Sum_{k=0..3^(n-1)} T(n, k) = A199923(n).
%F A199922 Sum_{k=0..3^(n-1)} (-1)^k * T(n, k) = A000007(n). (End)
%e A199922              1
%e A199922             1, 1
%e A199922          3, 1, 1, 3
%e A199922 9, 1, 1, 3, 1, 1, 3, 1, 1, 9
%p A199922 seq(print(seq(gcd(k,3^(n-1)), k=0..3^(n-1))),n=0..4);
%t A199922 T[n_, k_]:= If[n==0, 1, GCD[k, 3^(n-1)]];
%t A199922 Table[T[n, k], {n,0,6}, {k,0,3^(n-1)}]//Flatten (* _G. C. Greubel_, Nov 24 2023 *)
%o A199922 (Magma) [1] cat [Gcd(k, 3^(n-1)): k in [0..3^(n-1)], n in [1..6]]; // _G. C. Greubel_, Nov 24 2023
%o A199922 (SageMath)
%o A199922 def A199922(n,k): return gcd(k, 3^(n-1)) + (2/3)*int(n==0)
%o A199922 flatten([[A199922(n,k) for k in range(int(3^(n-1))+1)] for n in range(7)]) # _G. C. Greubel_, Nov 24 2023
%Y A199922 Cf. A000007, A198069, A199923.
%K A199922 nonn,tabf
%O A199922 0,4
%A A199922 _Peter Luschny_, Nov 12 2011