A347082 Dirichlet inverse of -A168036, n - A003415(n).

1, -1, -2, 1, -4, 3, -6, 3, 1, 5, -10, 0, -12, 7, 9, 9, -16, 1, -18, -2, 13, 11, -22, 1, 1, 13, 4, -4, -28, -13, -30, 27, 21, 17, 25, 6, -36, 19, 25, -5, -40, -19, -42, -8, -2, 23, -46, 6, 1, 1, 33, -10, -52, 5, 41, -11, 37, 29, -58, 3, -60, 31, -4, 81, 49, -31, -66, -14, 45, -33, -70, 22, -72, 37, 0, -16, 61, -37, -78

Offset

1,3

Links

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

Formula

a(1) = 1; and for n > 2, a(n) = Sum_{d|n, d<n} a(d) * A168036(n/d).

a(n) = A168036(n) + A347083(n).

a(n) = A347084(n) + A347086(n).

a(n) = A347087(n) - 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];

Crossrefs

Cf. A003415, A168036, A347083, A347084, A347086, A347087.

Cf. also A346241.

Sequence in context: A055631 A234586 A338657 * A186421 A351752 A361189

Adjacent sequences: A347079 A347080 A347081 * A347083 A347084 A347085

Keyword

sign

Author

Antti Karttunen, Aug 17 2021

Status

approved