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

1,7

Links

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

Formula

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

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

Mathematica

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

Prog

(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));

Crossrefs

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

Sequence in context: A090622 A035696 A170840 * A035630 A126723 A325846

Adjacent sequences: A300722 A300723 A300724 * A300726 A300727 A300728

Keyword

sign,look

Author

Antti Karttunen, Mar 11 2018

Status

approved