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

Author

Antti Karttunen, Mar 11 2018

Keywords

• nonn
• look

Links

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

Crossrefs

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

Programs

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 *)

PARI

A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
A300726(n) = -sumdiv(n,d,(dA053644(d));

Formula

a(n) = -Sum_{d|n, dA008683(n/d)*A053644(d).

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