OFFSET
1,3
COMMENTS
Multiplicative because A082903 is.
LINKS
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A082903(n/d) * a(d).
PROG
(PARI)
A082903(n) = (2^valuation(sigma(n), 2));
memoA366889 = Map();
A366889(n) = if(1==n, 1, my(v); if(mapisdefined(memoA366889, n, &v), v, v = -sumdiv(n, d, if(d<n, A082903(n/d)*A366889(d), 0)); mapput(memoA366889, n, v); (v)));
(Python)
from functools import lru_cache
from sympy import divisor_sigma, divisors
@lru_cache(maxsize=None)
def A366889(n): return 1 if n==1 else -sum((1<<(~(m:=int(divisor_sigma(d))) & m-1).bit_length())*A366889(n//d) for d in divisors(n, generator=True) if d>1) # Chai Wah Wu, Jan 03 2024
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jan 03 2024
STATUS
approved