%I #31 Oct 14 2023 14:05:54

%S 1,-1,1,-2,0,2,-1,-1,0,2,-4,0,0,0,4,2,-2,-2,0,0,2,-6,0,0,0,0,0,6,-1,

%T -1,0,-2,0,0,0,4,-2,0,-4,0,0,0,0,0,6,4,-4,0,0,-4,0,0,0,0,4,-10,0,0,0,

%U 0,0,0,0,0,0,10,2,2,-2,-4,0,-2,0,0,0,0,0,4

%N Triangle read by rows: T(n,k) = A023900(n/k)*phi(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).

%C Sum_{k=1..n} T(n,k) = A063524(n).

%F T(n,k) = A023900(n/k)*phi(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).

%e {

%e {1}, = 1

%e {-1, 1}, = 0

%e {-2, 0, 2}, = 0

%e {-1, -1, 0, 2}, = 0

%e {-4, 0, 0, 0, 4}, = 0

%e {2, -2, -2, 0, 0, 2}, = 0

%e {-6, 0, 0, 0, 0, 0, 6}, = 0

%e {-1, -1, 0, -2, 0, 0, 0, 4}, = 0

%e {-2, 0, -4, 0, 0, 0, 0, 0, 6}, = 0

%e {4, -4, 0, 0, -4, 0, 0, 0, 0, 4}, = 0

%e {-10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10}, = 0

%e {2, 2, -2, -4, 0, -2, 0, 0, 0, 0, 0, 4} = 0

%e }

%t nn = 12; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Flatten[Table[Table[If[Mod[n, k] == 0, g[n/k]*EulerPhi[k], 0], {k, 1, n}], {n, 1, nn}]]

%Y Cf. A000010, A023900, A366444, A054524, A054525, A063524, A054522, A054523, A129691, A127649.

%K sign,tabl

%O 1,4

%A _Mats Granvik_, Oct 12 2023