A378990 Dirichlet inverse of the binary weight of n (A000120).

1, -1, -2, 0, -2, 2, -3, 0, 2, 2, -3, 0, -3, 3, 4, 0, -2, -2, -3, 0, 9, 3, -4, 0, 1, 3, -4, 0, -4, -4, -5, 0, 10, 2, 9, 0, -3, 3, 8, 0, -3, -9, -4, 0, -4, 4, -5, 0, 6, -1, 4, 0, -4, 4, 7, 0, 8, 4, -5, 0, -5, 5, -18, 0, 10, -10, -3, 0, 13, -9, -4, 0, -3, 3, 0, 0, 14, -8, -5, 0, 9, 3, -4, 0, 4, 4, 11, 0, -4, 4, 13, 0, 15

Offset

1,3

Links

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

Index entries for sequences related to binary expansion of n

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A000120(n/d) * a(d).

a(n) = Sum_{d|n} A008683(d)*A378989(n/d).

Prog

(PARI)
memoA378990 = Map();
A378990(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378990, n, &v), v, v = -sumdiv(n, d, if(d<n, hammingweight(n/d)*A378990(d), 0)); mapput(memoA378990, n, v); (v)));

Crossrefs

Dirichlet inverse of A000120.

Möbius transform of A378989.

Cf. A008683, A378991.

Sequence in context: A103863 A387120 A166395 * A061199 A352128 A334203

Adjacent sequences: A378987 A378988 A378989 * A378991 A378992 A378993

Keyword

sign

Author

Antti Karttunen, Dec 15 2024

Status

approved