A378225 Dirichlet inverse of A067824.

1, -2, -2, 0, -2, 2, -2, 0, 0, 2, -2, 0, -2, 2, 2, 0, -2, 0, -2, 0, 2, 2, -2, 0, 0, 2, 0, 0, -2, -2, -2, 0, 2, 2, 2, 0, -2, 2, 2, 0, -2, -2, -2, 0, 0, 2, -2, 0, 0, 0, 2, 0, -2, 0, 2, 0, 2, 2, -2, 0, -2, 2, 0, 0, 2, -2, -2, 0, 2, -2, -2, 0, -2, 2, 0, 0, 2, -2, -2, 0, 0, 2, -2, 0, 2, 2, 2, 0, -2, 0, 2, 0, 2, 2, 2, 0, -2

Offset: 1

Author

Antti Karttunen, Nov 25 2024

Keywords

• sign

Comments

Möbius transform of A153881.

Links

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

Crossrefs

Cf. A008683, A067824, A153881.

Cf. also A378224.

Programs

PARI

A074206(n) = if(n>1, sumdiv(n, i, if(iA074206(i))), n); \\ From A074206
A067824(n) = sumdiv(n,d,A074206(d));
memoA378225 = Map();
A378225(n) = if(1==n,1,my(v); if(mapisdefined(memoA378225,n,&v), v, v = -sumdiv(n,d,if(dA067824(n/d)*A378225(d),0)); mapput(memoA378225,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA067824(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A153881(d).

Dirichlet g.f.: (2 - zeta(s)) / zeta(s). [See Dec 30 2018 formula in A067824]