A346478 Sum of A346476 and its Dirichlet inverse.

2, 0, 0, 1, 0, 2, 0, -3, 1, 6, 0, -11, 0, 6, 6, -5, 0, -23, 0, -29, 6, 18, 0, -3, 9, 18, -15, -37, 0, -60, 0, -9, 18, 30, 18, 23, 0, 30, 18, 1, 0, -84, 0, -83, -61, 34, 0, -13, 9, -67, 30, -91, 0, 45, 54, 5, 30, 54, 0, 75, 0, 50, -77, -5, 54, -184, 0, -137, 34, -176, 0, -13, 0, 66, -55, -145, 54, -188, 0, -37, 49

Offset: 1

Author

Antti Karttunen, Jul 30 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, A346477.

Cf. also A323911, A346250, A346480.

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];
A346478(n) = (A346476(n)+A346477(n));

Formula

a(n) = A346476(n) + A346477(n).

a(1) = 2; and for n > 2, a(n) = -Sum_{d|n, 1A346476(n/d) * A346477(d).