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%I #5 Mar 18 2019 07:29:04
%S 1,2,0,2,0,1,3,1,2,2,3,1,2,2,2,5,3,4,4,4,3,3,1,2,2,2,1,2,7,5,6,6,6,5,
%T 6,4,5,3,4,4,4,3,4,2,2,7,5,6,6,6,5,6,4,4,4,5,3,4,4,4,3,4,2,2,2,3,11,9,
%U 10,10,10,9,10,8,8,8,9,4,5,3,4,4,4,3,4,2,2,2,3,-2,2
%N T(n, k) = p(n) - (p(k) - t(k-1)) with t(n) = A000005(|n|) for n != 0 and t(0) = 0, p(n) = A000010(n) for n > 0 and p(0) = 0, for n >= 0 and 0 <= k <= n, triangle read by rows.
%H Peter Luschny, <a href="/A323226/a323226.png">Plot of the function</a>.
%e Triangle starts:
%e [0] 1
%e [1] 2, 0
%e [2] 2, 0, 1
%e [3] 3, 1, 2, 2
%e [4] 3, 1, 2, 2, 2
%e [5] 5, 3, 4, 4, 4, 3
%e [6] 3, 1, 2, 2, 2, 1, 2
%e [7] 7, 5, 6, 6, 6, 5, 6, 4
%e [8] 5, 3, 4, 4, 4, 3, 4, 2, 2
%e [9] 7, 5, 6, 6, 6, 5, 6, 4, 4, 4
%p with(numtheory):
%p T := (n, k) -> phi(n) - (phi(k) - tau(k-1)):
%p seq(seq(T(n, k), k=0..n), n=0..12);
%t phi[n_] := EulerPhi[n]; tau[n_] := If[n == 0, 0, DivisorSigma[0, n]];
%t T[n_, k_] := phi[n] - (phi[k] - tau[k - 1]);
%t Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten
%Y Cf. A000005, A000010.
%K sign,tabl,easy
%O 0,2
%A _Peter Luschny_, Feb 19 2019
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