%I #5 Apr 28 2021 14:44:10

%S 1,-2,0,-3,3,-5,5,-12,8,-12,16,-31,31,-55,23,-99,131,-184,184,-389,

%T 157,-528,760,-1171,800,-2058,1235,-3248,4442,-5566,5566,-13461,7433,

%U -20534,18290,-30439,38711,-77429,46895,-105973,136507,-187059,187059,-441337,185384,-632122,888075

%N a(1) = 1; a(n) = -Sum_{k=1..n} a(k/gcd(n,k)).

%F a(1) = 1; a(n) = -Sum_{d|n} Sum_{k=1..d, gcd(d,k) = 1} a(k).

%F a(n) = -a(n-1) if n belongs to A006512.

%t a[1] = 1; a[n_] := a[n] = -Sum[a[k/GCD[n, k]], {k, 1, n}]; Table[a[n], {n, 1, 47}]

%t a[1] = 1; a[n_] := a[n] = -Sum[Sum[If[GCD[k, d] == 1, a[k], 0], {k, 1, d}], {d, Divisors[n]}]; Table[a[n], {n, 1, 47}]

%Y Cf. A006512, A023900, A164306, A333613, A343761.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, Apr 28 2021