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A347085
Sum of A129283 and its Dirichlet inverse.
3
2, 0, 0, 9, 0, 24, 0, 21, 16, 36, 0, 22, 0, 48, 48, 49, 0, 34, 0, 36, 64, 72, 0, 63, 36, 84, 56, 50, 0, -26, 0, 113, 96, 108, 96, 102, 0, 120, 112, 101, 0, -30, 0, 78, 76, 144, 0, 156, 64, 90, 144, 92, 0, 126, 144, 139, 160, 180, 0, 203, 0, 192, 104, 257, 168, -38, 0, 120, 192, -34, 0, 230, 0, 228, 124, 134, 192
OFFSET
1,1
LINKS
FORMULA
a(n) = A129283(n) + A347084(n).
For n > 1, a(n) = -Sum_{d|n, 1<d<n} A129283(d) * A347084(n/d).
PROG
(PARI)
up_to = 16384;
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.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A129283(n) = (n + A003415(n));
v347084 = DirInverseCorrect(vector(up_to, n, A129283(n)));
A347084(n) = v347084[n];
A347085(n) = (A129283(n)+A347084(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Aug 17 2021
STATUS
approved