A349337 Dirichlet inverse of A230593.

1, -3, -4, 3, -6, 13, -8, -3, 4, 19, -12, -16, -14, 25, 25, 3, -18, -17, -20, -22, 33, 37, -24, 19, 6, 43, -4, -28, -30, -87, -32, -3, 49, 55, 49, 33, -38, 61, 57, 25, -42, -113, -44, -40, -29, 73, -48, -22, 8, -25, 73, -46, -54, 21, 73, 31, 81, 91, -60, 125, -62, 97, -37, 3, 85, -165, -68, -58, 97, -163, -72, -52

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• sign

Comments

Coincides with A347084 on all squarefree numbers (A005117), but also on n=81, where a(81) = A347084(81) = 4. Question: Are there any other such numbers?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A005117, A069359, A230593.

Cf. also A347084, A349434, A349435.

Programs

PARI

up_to = 20000;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA230593(n) = sumdiv(n, d, ((1==d)||isprime(d))*(n/d));
v349337 = DirInverseCorrect(vector(up_to,n,A230593(n)));
A349337(n) = v349337[n];

Formula

For n > 1, a(n) = -Sum_{d|n, 1A230593(d) * A349337(n/d).