A378528 - OEIS

%I #8 Dec 01 2024 13:41:05

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

%T -1,-1,0,-1,1,0,1,0,1,-1,1,0,1,-1,0,-1,-1,2,1,-1,1,-1,1,0,-1,-1,-1,0,

%U 1,0,1,-1,2,-1,1,2,0,0,0,-1,-1,0,0,-1,-1,-1,1,2,-1,0,0,-1,1,0,1,-1,2,0,1,0,1,-1,-2,0,-1,0,1,0,-1,-1,1,2,1,-1,0,-1,1,2

%N Dirichlet inverse of A378444.

%H Antti Karttunen, <a href="/A378528/b378528.txt">Table of n, a(n) for n = 1..20000</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378444(n/d) * a(d).

%F a(n) = Sum_{d|n} A000010(n/d)*A378527(d).

%F a(n) = Sum_{d|n} A008683(n/d)*A369974(d).

%o (PARI)

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

%o A369001(n) = !(A083345(n)%2);

%o A378444(n) = sumdiv(n,d,A369001(d));

%o memoA378528 = Map();

%o A378528(n) = if(1==n,1,my(v); if(mapisdefined(memoA378528,n,&v), v, v = -sumdiv(n,d,if(d<n,A378444(n/d)*A378528(d),0)); mapput(memoA378528,n,v); (v)));

%Y Cf. A000010, A008683, A378444, A378527.

%Y Möbius transform of A369974.

%K sign

%O 1,45

%A _Antti Karttunen_, Dec 01 2024