A378224 Dirichlet inverse of A378223.

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

Offset: 1

Author

Antti Karttunen, Nov 25 2024

Keywords

• sign

Comments

Möbius transform of A378218.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A008683, A345182, A378218, A378223.

Cf. also A378225.

Programs

PARI

memoA345182 = Map();
A345182(n) = if(n<=2, n%2, my(v); if(mapisdefined(memoA345182,n,&v), v, v = sumdiv(n,d,if(dA345182(d),0)); mapput(memoA345182,n,v); (v)));
A378223(n) = sumdiv(n,d,A345182(d));
memoA378224 = Map();
A378224(n) = if(1==n,1,my(v); if(mapisdefined(memoA378224,n,&v), v, v = -sumdiv(n,d,if(dA378223(n/d)*A378224(d),0)); mapput(memoA378224,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378223(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A378218(d).