A323886 Dirichlet inverse of A004718, Per Nørgård's "infinity sequence".

1, 1, -2, 0, 0, -2, -3, 0, 2, 0, -1, 0, 1, -3, -4, 0, 0, 2, -3, 0, 11, -1, -2, 0, -3, 1, 0, 0, 2, -4, -5, 0, 2, 0, -1, 0, 1, -3, -8, 0, -1, 11, -2, 0, 16, -2, -3, 0, 10, -3, -4, 0, -2, 0, -1, 0, 8, 2, 1, 0, 3, -5, -26, 0, 0, 2, -3, 0, 7, -1, -2, 0, -3, 1, 12, 0, 8, -8, -5, 0, -5, -1, -2, 0, 0, -2, -11, 0, -2, 16, -7, 0, 21, -3, -4, 0, -3, 10, 0, 0, 2, -4, -5, 0

Offset: 1

Author

Antti Karttunen, Feb 08 2019

Keywords

• sign

Comments

The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A004718, A323881, A323887.

Programs

Mathematica

b[0] = 0;
b[n_?EvenQ] := b[n] = -b[n/2];
b[n_] := b[n] = b[(n - 1)/2] + 1;
a[n_] := a[n] = If[n == 1, 1, -Sum[b[n/d] a[d], {d, Most@ Divisors[n]}]];
Array[a, 100] (* Jean-François Alcover, Feb 16 2020 *)

PARI

up_to = 65537;
A004718list(up_to) = { my(v=vector(up_to)); v[1]=1; v[2]=-1; for(n=3, up_to, v[n] = if(n%2, v[n>>1]+1, -v[n/2])); (v); }; \\ After code in A004718.
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(dA004718list(up_to));
A323886(n) = v323886[n];