A323887 Sum of Per Nørgård's "infinity sequence" (A004718) and its Dirichlet inverse (A323886).

2, 0, 0, 1, 0, -4, 0, -1, 4, 0, 0, 2, 0, -6, 0, 1, 0, 0, 0, 0, 12, -2, 0, -2, 0, 2, 0, 3, 0, -8, 0, -1, 4, 0, 0, 2, 0, -6, -4, 0, 0, 10, 0, 1, 16, -4, 0, 2, 9, -6, 0, -1, 0, 0, 0, -3, 12, 4, 0, 4, 0, -10, -20, 1, 0, 0, 0, 0, 8, -2, 0, -2, 0, 2, 12, 3, 6, -12, 0, 0, -4, -2, 0, 1, 0, -4, -8, -1, 0, 16, -6, 2, 20, -6, 0, -2, 0, 11, 0, 3, 0, -8, 0, 1, 28

Offset

1,1

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

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

Formula

a(n) = A004718(n) + A323886(n).

Prog

(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, 1+v[n>>1], -v[n/2])); (v); }; \\ After code in A004718.
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
v004718 = A004718list(up_to);
A004718(n) = v004718[n];
v323886 = DirInverse(v004718);
A323886(n) = v323886[n];
A323887(n) = (A004718(n)+A323886(n));

Crossrefs

Cf. A004718, A323886.

Cf. also A323365, A323882, A323885, A323896.

Sequence in context: A363929 A054876 A109502 * A349913 A346236 A323365

Adjacent sequences: A323884 A323885 A323886 * A323888 A323889 A323890

Keyword

sign

Author

Antti Karttunen, Feb 08 2019

Status

approved