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A353369
Sum of A103391 ("even fractal sequence") and its Dirichlet inverse.
3
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
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. also A349135, A353367.
Sequence in context: A365714 A221419 A140668 * A323900 A349347 A354187
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 18 2022
STATUS
approved