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

1,1

Links

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

Formula

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

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

Prog

(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(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A003602(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));

Crossrefs

Cf. A003602, A103391, A353368.

Cf. also A349135, A353367.

Sequence in context: A365714 A221419 A140668 * A323900 A349347 A354187

Adjacent sequences: A353366 A353367 A353368 * A353370 A353371 A353372

Keyword

sign

Author

Antti Karttunen, Apr 18 2022

Status

approved