A378218 Dirichlet inverse of A345182.

1, 0, -1, -1, -1, -2, -1, -2, -1, -2, -1, -3, -1, -2, -1, -3, -1, -2, -1, -3, -1, -2, -1, -4, -1, -2, -1, -3, -1, -2, -1, -4, -1, -2, -1, -3, -1, -2, -1, -4, -1, -2, -1, -3, -1, -2, -1, -5, -1, -2, -1, -3, -1, -2, -1, -4, -1, -2, -1, -3, -1, -2, -1, -5, -1, -2, -1, -3, -1, -2, -1, -4, -1, -2, -1, -3, -1, -2, -1, -5

Offset: 1

Author

Antti Karttunen, Nov 22 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A345182, A359508.

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)));
memoA378218 = Map();
A378218(n) = if(1==n,1,my(v); if(mapisdefined(memoA378218,n,&v), v, v = -sumdiv(n,d,if(dA345182(n/d)*A378218(d),0)); mapput(memoA378218,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA345182(n/d) * a(d).

Apparently, abs(a(n+1)) = A359508(n).