A378217 Dirichlet inverse of A330575.

1, -3, -4, 1, -6, 10, -8, 1, 2, 16, -12, -2, -14, 22, 22, 1, -18, -2, -20, -4, 30, 34, -24, -2, 4, 40, 2, -6, -30, -52, -32, 1, 46, 52, 46, -2, -38, 58, 54, -4, -42, -72, -44, -10, -8, 70, -48, -2, 6, -4, 70, -12, -54, -2, 70, -6, 78, 88, -60, 8, -62, 94, -12, 1, 82, -112, -68, -16, 94, -116, -72, -2, -74, 112, -8, -18, 94

Offset: 1

Author

Antti Karttunen, Nov 22 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A330575.

Programs

PARI

memoA330575 = Map();
A330575(n) = if(1==n,1,my(v); if(mapisdefined(memoA330575,n,&v), v, v = n + sumdiv(n,d,if(dA330575(d),0)); mapput(memoA330575,n,v); (v)));
memoA378217 = Map();
A378217(n) = if(1==n,1,my(v); if(mapisdefined(memoA378217,n,&v), v, v = -sumdiv(n,d,if(dA330575(n/d)*A378217(d),0)); mapput(memoA378217,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA330575(n/d) * a(d).