A346480 Sum of A250469 and its Dirichlet inverse.

2, 0, 0, 9, 0, 30, 0, 27, 25, 42, 0, 45, 0, 66, 70, 45, 0, 75, 0, 99, 110, 78, 0, 3, 49, 102, 125, 135, 0, 60, 0, 81, 130, 114, 154, -39, 0, 138, 170, 15, 0, 60, 0, 261, 175, 174, 0, 117, 121, 231, 190, 297, 0, -225, 182, 3, 230, 186, 0, -381, 0, 222, 275, 189, 238, 360, 0, 423, 290, 216, 0, 381, 0, 246, 245, 459

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. A250469, A346479.

Cf. also A346478.

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(dA250469(n)));
A346479(n) = v346479[n];
A346480(n) = (A250469(n)+A346479(n));

PARI

A346480(n) = if(1==n, 2, -sumdiv(n,d,if((1==d)||n==d,0,A250469(d)*A346479(n/d)))); \\ (Demonstrates the convolution formula).

Formula

a(n) = A250469(n) + A346479(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A250469(d) * A346479(n/d).