OFFSET
1,3
LINKS
Daniel R. Johnston, Nicol Leong, and Sebastian Tudzi, New bounds and progress towards a conjecture on the summatory function of (-2)^{Ω(n)}, arXiv:2408.04143 [math.NT], 2024.
Michael J. Mossinghoff and Timothy S. Trudgian, Oscillations in weighted arithmetic sums, arXiv:2007.14537 [math.NT], 2020.
Zhi-Wei Sun, On a pair of zeta functions, arXiv:1204.6689 [math.NT], 2012.
FORMULA
Johnston, Leong, & Tudzi prove that |a(n)| < 2260n. Sun conjectures that |a(n)| < n for n >= 3078. Mossinghoff & Trudgian verify this to 2.5 * 10^14.
Because of powers of two, |a(n)| >= n/2 infinitely often.
PROG
(PARI) s=0; vector(60, n, s+=(-2)^bigomega(n))
CROSSREFS
KEYWORD
sign
AUTHOR
Charles R Greathouse IV, Aug 09 2024
STATUS
approved