A346477 Dirichlet inverse of A346476.

1, -1, -1, 2, -3, 5, -3, 2, 8, 13, -9, -2, -9, 17, 11, 8, -15, -8, -15, -12, 19, 37, -17, 18, 8, 41, -4, -12, -27, -33, -25, 20, 37, 61, 25, 56, -33, 65, 35, 38, -39, -45, -39, -42, -36, 77, -41, 32, 32, -20, 53, -42, -47, 96, 35, 58, 61, 109, -57, 132, -55, 109, -48, 56, 43, -121, -63, -72, 71, -109, -69, 56

Offset: 1

Author

Antti Karttunen, Jul 29 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves

Crossrefs

Cf. A000040, A000720, A062234, A250469, A252748, A346476, A346478.

Cf. also A323910, A346248, A346479.

Programs

PARI

up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA346476(n) = (n+n-A250469(n));
v346477 = DirInverseCorrect(vector(up_to,n,A346476(n)));
A346477(n) = v346477[n];

Formula

a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, dA346476(n/d).

a(n) = A346478(n) - A346476(n).

a(p) = A252748(p) = A346248(p) = -A346476(p) = -A062234(A000720(p)), for any prime p.