A353368 Dirichlet inverse of A103391, "even fractal sequence".

1, -2, -2, 1, -2, 4, -3, -1, 2, 2, -4, -3, -3, 4, 3, 0, -2, -10, -6, 1, 8, 4, -7, 3, 1, -2, -8, -1, -5, -4, -9, -1, 14, -10, 2, 17, -6, 4, 1, -1, -4, -22, -12, 1, -3, 4, -13, -1, 6, -14, -6, 11, -8, 28, 1, 1, 19, -10, -16, 3, -9, 4, -25, -1, 10, -42, -18, 25, 18, 0, -19, -17, -6, -14, -12, 5, 13, 12, -21, 3, 24

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, A353369.

Cf. also A349134, A353366.

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];

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A103391(n/d) * a(d).

a(n) = A353369(n) - A103391(n).