A349920 Dirichlet g.f.: Product_{k>=2} (1 - mu(k)^2 * k^(-s)).

1, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 1, -1, 1, 1, 0, -1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 1, -1, 1, 0, 1, -1, 0, -1, 0, 1, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 1, 1, -1, -1

Offset

1

Comments

Dirichlet inverse of A050320.

Links

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

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A050320(n/d) * a(d).

Prog

(PARI)
A050320(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&issquarefree(d), s += A050320(n/d, d))); (s));
memoA349920 = Map();
A349920(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349920, n, &v), v, v = -sumdiv(n, d, if(d<n, A050320(n/d)*A349920(d), 0)); mapput(memoA349920, n, v); (v))); \\ Antti Karttunen, Dec 05 2021

Crossrefs

Cf. A008683, A050320, A114591, A114592, A129667.

Sequence in context: A294905 A353787 A297086 * A369253 A167752 A240025

Adjacent sequences: A349917 A349918 A349919 * A349921 A349922 A349923

Keyword

sign

Author

Ilya Gutkovskiy, Dec 05 2021

Status

approved