A271860 a(n) = -Sum_{i=1..n} (-1)^floor(n/i).

0, 1, 0, 3, 0, 3, 2, 5, 0, 5, 4, 7, 2, 5, 4, 11, 4, 7, 6, 9, 4, 11, 10, 13, 4, 9, 8, 15, 10, 13, 12, 15, 6, 13, 12, 19, 12, 15, 14, 21, 12, 15, 14, 17, 12, 23, 22, 25, 12, 17, 16, 23, 18, 21, 20, 27, 18, 25, 24, 27, 18, 21, 20, 31, 20, 27, 26, 29, 24, 31, 30

Offset: 0

Author

Wesley Ivan Hurt, Apr 15 2016

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=1 of A345033.

Cf. A000035, A075989.

Programs

Maple

A271860:=n->-add((-1)^floor(n/i), i=1..n): seq(A271860(n), n=0..100);

Mathematica

Table[-Sum[(-1)^Floor[n/i], {i, n}], {n, 0, 100}]

PARI

a(n) = -sum(i=1, n, (-1)^(n\i)); \\ Michel Marcus, Apr 16 2016

PARI

my(N=99, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^k*(1-x^k)/(1+x^k))/(1-x))) \\ Seiichi Manyama, Jun 06 2021

Python

from math import isqrt
def A271860(n): return (((t:=isqrt(m:=n>>1))**2<<1)-(s:=isqrt(n))**2+(sum(n//k for k in range(1,s+1))-(sum(m//k for k in range(1,t+1))<<1)<<1)<<1)-n # Chai Wah Wu, Oct 23 2023

Formula

a(2n) = 2*A075989(n) for n>0.

a(n) mod 2 = A000035(n).

a(n) = Sum_{k=1..n} (-1)^floor((n-k)/k). - Wesley Ivan Hurt, May 09 2021

G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + x^k). - Seiichi Manyama, Jun 06 2021