A378527 Dirichlet inverse of A378546.

1, -2, -3, 0, -5, 6, -7, 0, -1, 10, -11, -1, -13, 14, 14, -1, -17, 2, -19, -1, 20, 22, -23, 2, -1, 26, 3, -1, -29, -28, -31, 2, 32, 34, 34, 3, -37, 38, 38, 2, -41, -40, -43, -1, 8, 46, -47, 3, -1, 2, 50, -1, -53, -6, 54, 2, 56, 58, -59, 8, -61, 62, 10, 0, 64, -64, -67, -1, 68, -68, -71, -6, -73, 74, 8, -1, 76, -76, -79, 5

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A023900, A055615, A369974, A378546.

Cf. also A378525, A378526, A378528.

Programs

PARI

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
A378546(n) = sumdiv(n,d,d*A369001(n/d));
memoA378527 = Map();
A378527(n) = if(1==n,1,my(v); if(mapisdefined(memoA378527,n,&v), v, v = -sumdiv(n,d,if(dA378546(n/d)*A378527(d),0)); mapput(memoA378527,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378546(n/d) * a(d).

a(n) = Sum_{d|n} A055615(d)*A369974(n/d).

a(n) = Sum_{d|n} A023900(d)*A378528(n/d).