A378997 Dirichlet inverse of A057723.

1, -2, -3, -2, -5, 6, -7, 2, -3, 10, -11, 6, -13, 14, 15, 6, -17, 6, -19, 10, 21, 22, -23, -6, -5, 26, 6, 14, -29, -30, -31, 2, 33, 34, 35, 6, -37, 38, 39, -10, -41, -42, -43, 22, 15, 46, -47, -18, -7, 10, 51, 26, -53, -12, 55, -14, 57, 58, -59, -30, -61, 62, 21, -10, 65, -66, -67, 34, 69, -70, -71, -6, -73, 74, 15

Offset: 1

Author

Antti Karttunen, Dec 16 2024

Keywords

• sign
• mult

Links

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

Crossrefs

Cf. A057723.

Programs

PARI

A057723(n) = { my(f=factor(n)~); prod(i=1, #f, sigma(f[1, i]^f[2,i])-1); };
memoA378997 = Map();
A378997(n) = if(1==n,1,my(v); if(mapisdefined(memoA378997,n,&v), v, v = -sumdiv(n,d,if(dA057723(n/d)*A378997(d),0)); mapput(memoA378997,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA057723(n/d) * a(d).