A297115 Möbius transform of A000120, binary weight of n.

1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, -1, 0, 3, 0, 1, 0, 2, 0, 3, 0, 4, 0, -2, 0, -1, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 4, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 4, 0, 4, 0, 3, 0, -2, 0, 2, 0, -2, 0, 3, 0, 2, 0, -1, 0, -1, 0, 4, 0, -1, 0, 3, 0, 1, 0, 0, 0, 3, 0, 0, 0, -1, 0, 2, 0, 2, 0, 2, 0, 3, 0, 4, 0, 0

Offset: 1

Author

Antti Karttunen, Dec 26 2017

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A008683, A083254, A297114, A297116 (odd bisection), A297117.

Programs

PARI

A297115(n) = sumdiv(n,d,moebius(n/d)*hammingweight(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A000120(d).

a(n) = A083254(n) - A297114(n).

a(2n) = 0.