login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Dirichlet g.f.: Product_{k>=2} (1 - mu(k)^2 * k^(-s)).
1

%I #10 Jan 16 2022 15:21:44

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

%T 1,-1,0,0,0,0,-1,-1,0,0,0,-1,1,-1,1,1,0,-1,0,0,1,0,1,-1,0,0,0,0,0,-1,

%U 0,-1,0,1,0,0,1,-1,1,0,1,-1,0,-1,0,1,1,0,1,-1,0,0,0,-1,0,0,0,0,0,-1,0,0,1,0,0,0,0,-1,1,1,-1,-1

%N Dirichlet g.f.: Product_{k>=2} (1 - mu(k)^2 * k^(-s)).

%C Dirichlet inverse of A050320.

%H Antti Karttunen, <a href="/A349920/b349920.txt">Table of n, a(n) for n = 1..20000</a>

%F a(1) = 1; a(n) = -Sum_{d|n, d < n} A050320(n/d) * a(d).

%o (PARI)

%o A050320(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&issquarefree(d), s += A050320(n/d, d))); (s));

%o memoA349920 = Map();

%o A349920(n) = if(1==n,1,my(v); if(mapisdefined(memoA349920,n,&v), v, v = -sumdiv(n,d,if(d<n,A050320(n/d)*A349920(d),0)); mapput(memoA349920,n,v); (v))); \\ _Antti Karttunen_, Dec 05 2021

%Y Cf. A008683, A050320, A114591, A114592, A129667.

%K sign

%O 1

%A _Ilya Gutkovskiy_, Dec 05 2021