A378524 Dirichlet inverse of A333794.

1, -3, -6, 2, -12, 23, -20, 0, 14, 47, -36, -27, -40, 79, 102, 0, -48, -81, -64, -57, 174, 143, -96, 10, 68, 159, -24, -97, -112, -517, -116, 0, 314, 191, 360, 170, -128, 255, 350, 22, -144, -885, -176, -177, -400, 383, -240, 0, 218, -393, 414, -197, -216, 211, 656, 38, 566, 447, -284, 947, -232, 463, -696, 0, 724

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A052126, A333794.

Cf. also A378523.

Programs

PARI

A052126(n) = if(1==n,n,(n/vecmax(factor(n)[, 1])));
A333794(n) = if(1==n,n,n + A333794(n-A052126(n)));
memoA378524 = Map();
A378524(n) = if(1==n,1,my(v); if(mapisdefined(memoA378524,n,&v), v, v = -sumdiv(n,d,if(dA333794(n/d)*A378524(d),0)); mapput(memoA378524,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA333794(n/d) * a(d).