OFFSET
1,2
FORMULA
a(n) = (-1)^n*A308313(n).
Let A(n,k) = Sum_{j=1..n} j^k * floor(n/j). Then a(n) = 2^(n+1)*A(floor(n/2),n)-A(n,n).
MATHEMATICA
a[n_]:=Sum[ (-1)^k*k^n*Floor[n/k], {k, n}]; Array[a, 19] (* Stefano Spezia, Oct 29 2023 *)
PROG
(Python)
from math import isqrt
from sympy import bernoulli
def A366919(n): return ((((s:=isqrt(m:=n>>1))+1)*(bernoulli(n+1)-bernoulli(n+1, s+1))<<n+1)-((t:=isqrt(n))+1)*(bernoulli(n+1)-bernoulli(n+1, t+1))+(sum(w**n*(n+1)*((q:=m//w)+1)-bernoulli(n+1)+bernoulli(n+1, q+1) for w in range(1, s+1))<<n+1)-sum(w**n*(n+1)*((q:=n//w)+1)-bernoulli(n+1)+bernoulli(n+1, q+1) for w in range(1, t+1)))//(n+1)
(PARI) a(n) = sum(k=1, n, (-1)^k*k^n*(n\k)); \\ Michel Marcus, Oct 29 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Chai Wah Wu, Oct 28 2023
STATUS
approved