A378528 Dirichlet inverse of A378444.

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, -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, 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

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A008683, A378444, A378527.

Möbius transform of A369974.

Programs

PARI

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
A378444(n) = sumdiv(n,d,A369001(d));
memoA378528 = Map();
A378528(n) = if(1==n,1,my(v); if(mapisdefined(memoA378528,n,&v), v, v = -sumdiv(n,d,if(dA378444(n/d)*A378528(d),0)); mapput(memoA378528,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378444(n/d) * a(d).

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

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