A353335 Dirichlet inverse of A353420.

1, -1, -2, 0, -3, 2, -4, 0, -5, 3, -5, 0, -6, 4, 0, 0, -7, 5, -8, 0, -3, 5, -10, 0, -8, 6, -14, 0, -11, 0, -13, 0, -2, 7, -2, 0, -14, 8, -5, 0, -15, 3, -16, 0, 7, 10, -18, 0, -25, 8, -4, 0, -20, 14, -1, 0, -7, 11, -21, 0, -23, 13, 8, 0, -4, 2, -24, 0, -9, 2, -25, 0, -27, 14, 4, 0, -8, 5, -28, 0, -52, 15, -30, 0, -3

Offset: 1

Author

Antti Karttunen, Apr 20 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A126760, A353420, A353336.

Programs

PARI

up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A353420(n) = A126760(A003961(n));
v353335 = DirInverseCorrect(vector(up_to,n,A353420(n)));
A353335(n) = v353335[n];

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A353420(n/d) * a(d).

a(n) = A353336(n) - A353420(n).