A300725 - OEIS

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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 (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 A325846` `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 March 25 15:28 EDT 2023. Contains 361526 sequences. (Running on oeis4.)