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A343761 a(1) = 1; a(n) = -Sum_{k=1..n, gcd(n,k) > 1} a(n/gcd(n,k)).

%I A343761 #9 Dec 21 2022 16:51:24
%S A343761 1,-1,-1,0,-1,2,-1,0,1,4,-1,-2,-1,6,5,0,-1,-8,-1,-12,7,10,-1,6,3,12,
%T A343761 -5,-30,-1,-54,-1,0,11,16,9,48,-1,18,13,84,-1,-116,-1,-90,-41,22,-1,
%U A343761 -42,5,-72,17,-132,-1,130,13,330,19,28,-1,482,-1,30,-83,0,15,-312,-1,-240,23,-258
%N A343761 a(1) = 1; a(n) = -Sum_{k=1..n, gcd(n,k) > 1} a(n/gcd(n,k)).
%H A343761 Robert Israel, <a href="/A343761/b343761.txt">Table of n, a(n) for n = 1..10000</a>
%F A343761 a(1) = 1; a(n) = -Sum_{d|n, d < n} phi(d) * a(d).
%p A343761 f:= proc(n) option remember; local G,g;
%p A343761   G:= subs(1=NULL, map(igcd,[$1..n],n));
%p A343761   -add(procname(n/g), g=G);
%p A343761 end proc:
%p A343761 f(1):= 1:
%p A343761 map(f, [$1..100]); # _Robert Israel_, Dec 21 2022
%t A343761 a[1] = 1; a[n_] := a[n] = -Sum[If[GCD[n, k] > 1, a[n/GCD[n, k]], 0], {k, 1, n}]; Table[a[n], {n, 1, 70}]
%t A343761 a[1] = 1; a[n_] := -Sum[If[d < n, EulerPhi[d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 70}]
%Y A343761 Cf. A000010, A023900, A054531, A332792, A343762.
%K A343761 sign,look
%O A343761 1,6
%A A343761 _Ilya Gutkovskiy_, Apr 28 2021