A300725 Möbius transform of A053645(n), distance to the largest power of 2 less than or equal to n.

0, 0, 1, 0, 1, 1, 3, 0, 0, 1, 3, 2, 5, 3, 5, 0, 1, 0, 3, 2, 1, 3, 7, 4, 8, 5, 10, 6, 13, 5, 15, 0, -3, 1, -1, 0, 5, 3, 1, 4, 9, 1, 11, 6, 6, 7, 15, 8, 14, 8, 17, 10, 21, 10, 19, 12, 21, 13, 27, 10, 29, 15, 26, 0, -5, -3, 3, 2, -3, -1, 7, 0, 9, 5, -4, 6, 7, 1, 15, 8, 6, 9, 19, 2, 19, 11, 9, 12, 25, 6, 19, 14, 13, 15, 27

Offset: 1

Author

Antti Karttunen, Mar 11 2018

Keywords

• sign
• look

Links

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

Crossrefs

Cf. A000010, A008683, A053644, A053645, A297111, A297115, A300723, A300724.

Programs

Mathematica

With[{s = Array[# - 2^Floor@ Log2@ # &, 95]}, Table[DivisorSum[n, MoebiusMu[n/#] s[[#]] &], {n, Length@ s}]] (* Michael De Vlieger, Mar 13 2018 *)

PARI

A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
A053645(n) = (n-A053644(n));
A300725(n) = sumdiv(n,d,moebius(n/d)*A053645(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A053645(d).

a(n) + A300724(n) = A000010(n).