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

Author

Antti Karttunen, Aug 18 2021

Keywords

• nonn

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

Crossrefs

Cf. A030059, A030229, A332844, A347090.

Cf. also A347093.

Programs

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(dA332844(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));

Formula

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

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

For all n >= 1, a(A030059(n)) = 0, a(A030229(n)) = 2*A332844(A030229(n)).