A323896 Sum of binary Gray code A003188 and its Dirichlet inverse, A323895.

2, 0, 0, 9, 0, 12, 0, 9, 4, 42, 0, 0, 0, 24, 28, 27, 0, 62, 0, -15, 16, 84, 0, 33, 49, 66, 44, -6, 0, -74, 0, 45, 56, 150, 56, -4, 0, 156, 44, 123, 0, 118, 0, -36, 130, 168, 0, 24, 16, -105, 100, -27, 0, -62, 196, 69, 104, 114, 0, 230, 0, 96, 180, 99, 154, 46, 0, -69, 112, 42, 0, 186, 0, 330, -98, -72, 112, 118, 0, 39, 117, 366, 0, 47

Offset

1,1

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) = A003188(n) + A323895(n).

Prog

(PARI)
up_to = 65537;
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.
A003188(n) = bitxor(n, n>>1);
v323895 = DirInverse(vector(up_to, n, A003188(n)));
A323895(n) = v323895[n];
A323896(n) = (A003188(n)+A323895(n));

Crossrefs

Cf. A003188, A323895.

Cf. also A323365, A323412, A323885, A323887, A323894.

Sequence in context: A230878 A349369 A349352 * A345065 A323364 A323403

Adjacent sequences: A323893 A323894 A323895 * A323897 A323898 A323899

Keyword

sign

Author

Antti Karttunen, Feb 08 2019

Status

approved