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A300726 Difference between A053644 (the largest power of 2 less than or equal to n) and its Möbius transform. 2
0, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 6, 1, 5, 5, 8, 1, 10, 1, 10, 5, 9, 1, 12, 4, 9, 8, 10, 1, 13, 1, 16, 9, 17, 7, 20, 1, 17, 9, 20, 1, 21, 1, 18, 14, 17, 1, 24, 4, 20, 17, 18, 1, 24, 11, 20, 17, 17, 1, 26, 1, 17, 22, 32, 11, 41, 1, 34, 17, 39, 1, 40, 1, 33, 20, 34, 11, 41, 1, 40, 16, 33, 1, 42, 19, 33, 17, 36, 1, 46, 11, 34, 17, 33, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A053644(d).

a(n) = A053644(n) - A300724(n).

MATHEMATICA

With[{s = Array[2^Floor@ Log2@ # &, 95]}, Table[s[[n]] - 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

A300726(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A053644(d));

CROSSREFS

Cf. A008683, A053644, A300724, A300725, A300244.

Sequence in context: A329480 A277895 A328772 * A325352 A305438 A078898

Adjacent sequences:  A300723 A300724 A300725 * A300727 A300728 A300729

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Mar 11 2018

STATUS

approved

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Last modified July 9 15:32 EDT 2020. Contains 335543 sequences. (Running on oeis4.)