A366939 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(k+3,4) * floor(n/k).

1, -3, 13, -26, 45, -70, 141, -228, 283, -366, 636, -879, 942, -1232, 1914, -2331, 2515, -3090, 4226, -5313, 5539, -6114, 8837, -10558, 9988, -11947, 15969, -17705, 18256, -20364, 26013, -30592, 29330, -31874, 42222, -47034, 44357, -49602, 64164, -69115, 66637, -74017

Offset: 1

Author

Seiichi Manyama, Oct 29 2023

Keywords

• sign

Crossrefs

Cf. A024919, A366937, A366938.

Cf. A365439, A366723.

Programs

PARI

a(n) = sum(k=1, n, (-1)^(k-1)*binomial(k+3, 4)*(n\k));

Python

from math import isqrt
from sympy import rf
def A366939(n): return ((rf(s:=isqrt(m:=n>>1),3)*(s+1)*((s**2<<2)+13*s+8)<<3)-rf(t:=isqrt(n),5)*(t+1)+sum((((q:=m//w)+1)*(-q*(q+2)*((q**2<<2)+13*q+8)-5*w*(w+1)*((r:=w<<1)+1)*(r+3))<<3) for w in range(1,s+1))+sum(rf(q:=n//w,5)+5*(q+1)*rf(w,4) for w in range(1,t+1)))//120 # Chai Wah Wu, Oct 29 2023

Formula

G.f.: 1/(1-x) * Sum_{k>=1} x^k/(1+x^k)^5 = -1/(1-x) * Sum_{k>=1} binomial(k+3,4) * (-x)^k/(1-x^k).