A353369 Sum of A103391 ("even fractal sequence") and its Dirichlet inverse.

2, 0, 0, 4, 0, 8, 0, 4, 4, 8, 0, 4, 0, 12, 8, 9, 0, 0, 0, 12, 12, 16, 0, 16, 4, 12, 0, 14, 0, 12, 0, 16, 16, 8, 12, 36, 0, 24, 12, 20, 0, 0, 0, 24, 4, 28, 0, 24, 9, 12, 8, 38, 0, 56, 16, 30, 24, 20, 0, 34, 0, 36, -8, 32, 12, -8, 0, 60, 28, 36, 0, 20, 0, 24, 8, 44, 24, 52, 0, 44, 28, 16, 0, 74, 8, 48, 20, 44, 0, 52

Offset: 1

Author

Antti Karttunen, Apr 18 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003602, A103391, A353368.

Cf. also A349135, A353367.

Programs

PARI

up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003602(n) = (n/2^valuation(n, 2)+1)/2; \\ From A003602
A103391(n) = if(1==n,1,(1+A003602(n-1)));
v353368 = DirInverseCorrect(vector(up_to,n,A103391(n)));
A353368(n) = v353368[n];
A353369(n) = (A103391(n)+A353368(n));

Formula

a(n) = A103391(n) + A353368(n).

For n > 1, a(n) = -Sum_{d|n, 1A103391(d) * A353368(n/d).