A065651 a(n) = Sum_{k=1..n} (-1)^tau(k) = n - 2*floor(sqrt(n)).

0, 1, 0, 1, 2, 3, 4, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 14, 15, 16, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59

Offset: 2

Author

Vladeta Jovovic, Dec 03 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000005 (tau), A000196, A028391, A028392.

Programs

Mathematica

Table[n-2*Floor[Sqrt[n]],{n,2,80}] (* Harvey P. Dale, Jul 27 2012 *)

PARI

a(n) = n - 2*sqrtint(n); \\ Harry J. Smith, Oct 25 2009

Python

import math
def a(n): return n - 2 * math.isqrt(n) # Darío Clavijo, Apr 23 2023