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A353367
Sum of A110963 and its Dirichlet inverse.
4
2, 0, 0, 1, 0, 2, 0, 1, 1, 4, 0, 1, 0, 2, 4, 1, 0, 5, 0, 2, 2, 4, 0, 1, 4, 8, 5, 1, 0, -2, 0, 1, 4, 10, 4, 3, 0, 6, 8, 2, 0, 10, 0, 2, 8, 4, 0, 1, 1, 10, 10, 4, 0, 3, 8, 1, 6, 16, 0, 1, 0, 2, 15, 1, 16, 14, 0, 5, 4, 6, 0, 3, 0, 20, 6, 3, 4, -2, 0, 2, 9, 22, 0, 6, 20, 12, 16, 2, 0, 16, 8, 2, 2, 4, 12, 1, 0, 25, 24
OFFSET
1,1
COMMENTS
Note the negative terms, in contrast to A349135, which apparently has none.
LINKS
FORMULA
a(n) = A110963(n) + A353366(n).
For n > 1, a(n) = -Sum_{d|n, 1<d<n} A110963(d) * A353366(n/d).
For all n >= 1, a(4*n) = A110963(n), and a(8*n-4) = A003602(n).
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) = (1+(n>>valuation(n, 2)))/2;
A110963(n) = if(n%2, A003602((1+n)/2), A110963(n/2));
v353366 = DirInverseCorrect(vector(up_to, n, A110963(n)));
A353366(n) = v353366[n];
A353367(n) = (A110963(n)+A353366(n));
CROSSREFS
Cf. also A349135, A353369.
Sequence in context: A349912 A345079 A307377 * A349439 A323882 A349446
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 18 2022
STATUS
approved