OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} [gcd(k, n) = 1] * (-2)^k, where [] is the Iverson bracket.
MAPLE
MATHEMATICA
A367545[n_]:=Sum[(-2)^k*Boole[CoprimeQ[n, k]], {k, 0, n}];
Array[A367545, 50, 0] (* Paolo Xausa, Nov 24 2023 *)
PROG
(SageMath). # For Python include 'import math' for math.gcd.
def a(n):
cop = [int(gcd(i, n) == 1) for i in range(n + 1)]
return sum(p * (-2)^k for k, p in enumerate(cop))
print([a(n) for n in range(34)])
(PARI) a(n) = sum(k=0, n, (-2)^k*abs(kronecker(n-k, k))); \\ Michel Marcus, Nov 23 2023
(Python)
from math import gcd
def A367545(n): return sum((-(1<<k) if k&1 else 1<<k) for k in range(n+1) if gcd(n, k)==1) # Chai Wah Wu, Nov 24 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Nov 22 2023
STATUS
approved