A347091 Sum of A332844 and its Dirichlet inverse.

2, 0, 0, 9, 0, 24, 0, 21, 16, 36, 0, 28, 0, 48, 48, 37, 0, 36, 0, 42, 64, 72, 0, 60, 36, 84, 48, 56, 0, 0, 0, 81, 96, 108, 96, 114, 0, 120, 112, 90, 0, 0, 0, 84, 72, 144, 0, 164, 64, 84, 144, 98, 0, 120, 144, 120, 160, 180, 0, 216, 0, 192, 96, 166, 168, 0, 0, 126, 192, 0, 0, 258, 0, 228, 112, 140, 192, 0, 0, 246, 132

Offset

1,1

Comments

No negative terms in range 1 .. 2^20.

Apparently, A030059 gives the positions of all zeros.

Links

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

Formula

a(n) = A332844(n) + A347090(n).

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A332844(d) * A347090(n/d).

For all n >= 1, a(A030059(n)) = 0, a(A030229(n)) = 2*A332844(A030229(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.
A332844(n) = sumdiv(n, d, issquare(n/d) * sigma(d));
v347090 = DirInverseCorrect(vector(up_to, n, A332844(n)));
A347090(n) = v347090[n];
A347091(n) = (A332844(n)+A347090(n));

Crossrefs

Cf. A030059, A030229, A332844, A347090.

Cf. also A347093.

Sequence in context: A323403 A346238 A347085 * A347229 A347095 A346255

Adjacent sequences: A347088 A347089 A347090 * A347092 A347093 A347094

Keyword

nonn

Author

Antti Karttunen, Aug 18 2021

Status

approved