A359433 Dirichlet inverse of A071773.

1, -1, -1, -1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 1, 1, 1, -1, 2, -1, 1, 1, 1, -1, -1, -4, 1, 2, 1, -1, -1, -1, -1, 1, 1, 1, 2, -1, 1, 1, -1, -1, -1, -1, 1, 2, 1, -1, -1, -6, 4, 1, 1, -1, -2, 1, -1, 1, 1, -1, -1, -1, 1, 2, -1, 1, -1, -1, 1, 1, -1, -1, -2, -1, 1, 4, 1, 1, -1, -1, -1, 4, 1, -1, -1, 1, 1, 1, -1, -1, -2, 1, 1, 1, 1, 1, 1, -1, 6, 2, 4, -1, -1, -1, -1, -1

Offset: 1

Author

Antti Karttunen, Jan 02 2023

Keywords

• sign
• mult

Comments

Multiplicative because A071773 is.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A071773.

Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).

Cf. also A359432.

Programs

Mathematica

f[p_, e_] := (-1)^e * (1-p)^Floor[e/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 04 2023 *)

PARI

A071773(n) = { my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]>1)); };
memoA359433 = Map();
A359433(n) = if(1==n,1,my(v); if(mapisdefined(memoA359433,n,&v), v, v = -sumdiv(n,d,if(dA071773(n/d)*A359433(d),0)); mapput(memoA359433,n,v); (v)));

Formula

Multiplicative with a(p^e) = (-1)^e * (1-p)^floor(e/2). - Sebastian Karlsson, Jan 03 2023