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A300725 Möbius transform of A053645(n), distance to the largest power of 2 less than or equal to n. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A235794

Adjacent sequences:  A300722 A300723 A300724 * A300726 A300727 A300728

KEYWORD

sign,look

AUTHOR

Antti Karttunen, Mar 11 2018

STATUS

approved

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Last modified February 20 20:53 EST 2019. Contains 320345 sequences. (Running on oeis4.)