login
a(n) = Sum_{d|n} (-1)^phi(d) * mu(n/d).
1

%I #5 Jun 22 2024 22:30:33

%S -1,0,2,2,2,0,2,0,0,0,2,-2,2,0,-2,0,2,0,2,-2,-2,0,2,0,0,0,0,-2,2,0,2,

%T 0,-2,0,-2,0,2,0,-2,0,2,0,2,-2,0,0,2,0,0,0,-2,-2,2,0,-2,0,-2,0,2,2,2,

%U 0,0,0,-2,0,2,-2,-2,0,2,0,2,0,0,-2,-2,0,2,0,0,0,2,2,-2,0,-2,0,2

%N a(n) = Sum_{d|n} (-1)^phi(d) * mu(n/d).

%C Möbius transform of (-1)^phi(n) (which equals -1 if 1 <= n <= 2, and 1 if n >= 3).

%t Table[DivisorSum[n, (-1)^EulerPhi[#] MoebiusMu[n/#] &], {n, 100}]

%Y Cf. A000010 (phi), A008683 (mu), A373925.

%K sign

%O 1,3

%A _Wesley Ivan Hurt_, Jun 22 2024