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A347083
Sum of -A168036 and its Dirichlet inverse.
4
2, 0, 0, 1, 0, 4, 0, -1, 4, 8, 0, -4, 0, 12, 16, -7, 0, -2, 0, -6, 24, 20, 0, -19, 16, 24, 4, -8, 0, -14, 0, -21, 40, 32, 48, -18, 0, 36, 48, -33, 0, -18, 0, -12, 4, 44, 0, -58, 36, 6, 64, -14, 0, -22, 80, -47, 72, 56, 0, -29, 0, 60, 8, -47, 96, -26, 0, -18, 88, -22, 0, -62, 0, 72, 20, -20, 120, -30, 0, -108, -11, 80
OFFSET
1,1
LINKS
FORMULA
a(n) = A347082(n) - A168036(n).
For n > 1, a(n) = Sum_{d|n, 1<d<n} A168036(d) * A347082(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]));
A168036(n) = (A003415(n)-n);
v347082 = DirInverseCorrect(vector(up_to, n, -A168036(n)));
A347082(n) = v347082[n];
A347083(n) = (A347082(n)-A168036(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Aug 17 2021
STATUS
approved