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A366444 Triangle read by rows: T(n,k) = phi(n/k)*A023900(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).

%I A366444 #21 Oct 14 2023 14:05:17
%S A366444 1,1,-1,2,0,-2,2,-1,0,-1,4,0,0,0,-4,2,-2,-2,0,0,2,6,0,0,0,0,0,-6,4,-2,
%T A366444 0,-1,0,0,0,-1,6,0,-4,0,0,0,0,0,-2,4,-4,0,0,-4,0,0,0,0,4,10,0,0,0,0,0,
%U A366444 0,0,0,0,-10,4,-2,-4,-2,0,2,0,0,0,0,0,2
%N A366444 Triangle read by rows: T(n,k) = phi(n/k)*A023900(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
%C A366444 Sum_{k=1..n} T(n,k) = A063524(n).
%F A366444 T(n,k) = phi(n/k)*A023900(k) if k divides n, T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n).
%e A366444 {
%e A366444 {1}, = 1
%e A366444 {1, -1}, = 0
%e A366444 {2, 0, -2}, = 0
%e A366444 {2, -1, 0, -1}, = 0
%e A366444 {4, 0, 0, 0, -4}, = 0
%e A366444 {2, -2, -2, 0, 0, 2}, = 0
%e A366444 {6, 0, 0, 0, 0, 0, -6}, = 0
%e A366444 {4, -2, 0, -1, 0, 0, 0, -1}, = 0
%e A366444 {6, 0, -4, 0, 0, 0, 0, 0, -2}, = 0
%e A366444 {4, -4, 0, 0, -4, 0, 0, 0, 0, 4}, = 0
%e A366444 {10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}, = 0
%e A366444 {4, -2, -4, -2, 0, 2, 0, 0, 0, 0, 0, 2} = 0
%e A366444 }
%t A366444 nn = 12; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Flatten[Table[Table[If[Mod[n, k] == 0, EulerPhi[n/k]*g[k], 0], {k, 1, n}], {n, 1, nn}]]
%Y A366444 Cf. A000010, A023900, A366445, A054524, A054525, A063524, A054522, A054523, A129691, A127649.
%K A366444 sign,tabl
%O A366444 1,4
%A A366444 _Mats Granvik_, Oct 12 2023