A331739 a(n) is n minus its largest odd divisor.

0, 1, 0, 3, 0, 3, 0, 7, 0, 5, 0, 9, 0, 7, 0, 15, 0, 9, 0, 15, 0, 11, 0, 21, 0, 13, 0, 21, 0, 15, 0, 31, 0, 17, 0, 27, 0, 19, 0, 35, 0, 21, 0, 33, 0, 23, 0, 45, 0, 25, 0, 39, 0, 27, 0, 49, 0, 29, 0, 45, 0, 31, 0, 63, 0, 33, 0, 51, 0, 35, 0, 63, 0, 37, 0, 57, 0, 39, 0, 75, 0, 41, 0, 63, 0, 43, 0, 77, 0, 45, 0, 69, 0, 47

Offset: 1

Author

Antti Karttunen, Feb 02 2020

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000265, A006519, A007814, A135481.

Cf. A129527 (even bisection).

Programs

Maple

A331739 := proc(n)
    n-A000265(n) ;
end proc:
seq(A331739(n),n=1..40) ; # R. J. Mathar, Jan 24 2022

Mathematica

a[n_] := n - n/2^IntegerExponent[n, 2];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 19 2023 *)

PARI

A331739(n) = (n-(n>>valuation(n,2)));

Python

def A331739(n): return n-(n>>(~n & n-1).bit_length()) # Chai Wah Wu, Jul 01 2022

Formula

a(n) = n - A000265(n).

Sum_{k=1..n} a(k) ~ n^2/6. - Amiram Eldar, Sep 13 2024