A347087 Sum of n and the Dirichlet inverse of n - A003415(n).

2, 1, 1, 5, 1, 9, 1, 11, 10, 15, 1, 12, 1, 21, 24, 25, 1, 19, 1, 18, 34, 33, 1, 25, 26, 39, 31, 24, 1, 17, 1, 59, 54, 51, 60, 42, 1, 57, 64, 35, 1, 23, 1, 36, 43, 69, 1, 54, 50, 51, 84, 42, 1, 59, 96, 45, 94, 87, 1, 63, 1, 93, 59, 145, 114, 35, 1, 54, 114, 37, 1, 94, 1, 111, 75, 60, 138, 41, 1, 68, 97, 123, 1, 87

Offset

1,1

Comments

The first negative term is a(1408) = -131.

Links

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

Formula

a(n) = n + A347082(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];
A347087(n) = (n+A347082(n));

Crossrefs

Cf. A003415, A168036, A347082, A347083, A347086.

Sequence in context: A136789 A342916 A339966 * A022661 A120292 A179318

Adjacent sequences: A347084 A347085 A347086 * A347088 A347089 A347090

Keyword

sign

Author

Antti Karttunen, Aug 17 2021

Status

approved