A347086 Difference between the Dirichlet inverse of -A168036, n - A003415(n) and the Dirichlet inverse of A129283, n + A003415(n), where A003415 is the Arithmetic derivative of n.

0, 2, 2, 0, 2, -10, 2, 2, 0, -14, 2, 6, 2, -18, -16, 8, 2, 6, 2, 6, -20, -26, 2, 6, 0, -30, 2, 6, 2, 74, 2, 26, -28, -38, -24, 0, 2, -42, -32, 2, 2, 94, 2, 6, 6, -50, 2, 10, 0, 6, -40, 6, 2, 14, -32, -2, -44, -62, 2, -48, 2, -66, 6, 80, -36, 134, 2, 6, -52, 130, 2, 20, 2, -78, 6, 6, -36, 154, 2, -6, 12, -86, 2, -60

Offset

1,2

Links

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

Formula

a(n) = A347082(n) - A347084(n).

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]));
v347082 = DirInverseCorrect(vector(up_to, n, n-A003415(n)));
A347082(n) = v347082[n];
v347084 = DirInverseCorrect(vector(up_to, n, n+A003415(n)));
A347084(n) = v347084[n];
A347086(n) = (A347082(n)-A347084(n));

Crossrefs

Cf. A003415, A129283, A168036, A347082, A347084.

Sequence in context: A011218 A171244 A028305 * A137349 A087318 A087319

Adjacent sequences: A347083 A347084 A347085 * A347087 A347088 A347089

Keyword

sign

Author

Antti Karttunen, Aug 17 2021

Status

approved