A347085 Sum of A129283 and its Dirichlet inverse.

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

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

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

Cf. A003415, A129283, A347083, A347084, A347086.

Sequence in context: A323364 A323403 A346238 * A347091 A347229 A347095

Adjacent sequences: A347082 A347083 A347084 * A347086 A347087 A347088

Keyword

sign

Author

Antti Karttunen, Aug 17 2021

Status

approved