A354821 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA342001(n/d) * a(d).

1, -1, -1, -1, -1, -3, -1, 0, -1, -5, -1, 3, -1, -7, -6, 1, -1, 4, -1, 3, -8, -11, -1, 8, -1, -13, 0, 3, -1, 3, -1, 1, -12, -17, -10, 17, -1, -19, -14, 12, -1, 1, -1, 3, 4, -23, -1, 3, -1, 6, -18, 3, -1, 8, -14, 16, -20, -29, -1, 62, -1, -31, 4, 0, -16, -3, -1, 3, -24, -9, -1, -6, -1, -37, 6, 3, -16, -5, -1, 7, 1

Offset: 1

Author

Antti Karttunen, Jun 08 2022

Keywords

• sign

Comments

Dirichlet inverse of pointwise sum of A342001 (arithmetic derivative of n / A003557(n)) and A063524 (1, 0, 0, 0, ...).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A003415, A003557, A063524, A342001.

Cf. also A346241.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
memoA354821 = Map();
A354821(n) = if(1==n,1,my(v); if(mapisdefined(memoA354821,n,&v), v, v = -sumdiv(n,d,if(dA342001(n/d)*A354821(d),0)); mapput(memoA354821,n,v); (v)));