A300726 Difference between A053644 (the largest power of 2 less than or equal to n) and its Möbius transform.

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

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