A378989 Dirichlet inverse of the Möbius transform of binary weight of n.

1, 0, -1, 0, -1, 0, -2, 0, 1, 0, -2, 0, -2, 0, 1, 0, -1, 0, -2, 0, 5, 0, -3, 0, 0, 0, -3, 0, -3, 0, -4, 0, 6, 0, 5, 0, -2, 0, 4, 0, -2, 0, -3, 0, -1, 0, -4, 0, 4, 0, 1, 0, -3, 0, 3, 0, 4, 0, -4, 0, -4, 0, -11, 0, 6, 0, -2, 0, 8, 0, -3, 0, -2, 0, 2, 0, 9, 0, -4, 0, 6, 0, -3, 0, 1, 0, 6, 0, -3, 0, 8, 0, 9, 0, 2, 0, -2, 0, -12, 0, -3, 0, -4, 0, -12

Offset

1,7

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} A297115(n/d) * a(d).

a(n) = Sum_{d|n} A378990(d).

Prog

(PARI)
A297115(n) = sumdiv(n, d, moebius(n/d)*hammingweight(d));
memoA378989 = Map();
A378989(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378989, n, &v), v, v = -sumdiv(n, d, if(d<n, A297115(n/d)*A378989(d), 0)); mapput(memoA378989, n, v); (v)));

Crossrefs

Dirichlet inverse of A297115.

Inverse Möbius transform of A378990.

Cf. A000120.

Sequence in context: A286351 A091394 A029881 * A347290 A070090 A230642

Adjacent sequences: A378986 A378987 A378988 * A378990 A378991 A378992

Keyword

sign

Author

Antti Karttunen, Dec 15 2024

Status

approved