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A375286
a(n) = f(1) + f(2) + ... + f(n), where f(n) = (-2)^Omega(n) = A165872(n).
0
1, -1, -3, 1, -1, 3, 1, -7, -3, 1, -1, -9, -11, -7, -3, 13, 11, 3, 1, -7, -3, 1, -1, 15, 19, 23, 15, 7, 5, -3, -5, -37, -33, -29, -25, -9, -11, -7, -3, 13, 11, 3, 1, -7, -15, -11, -13, -45, -41, -49, -45, -53, -55, -39, -35, -19, -15, -11, -13, 3, 1, 5, -3, 61
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
Partial sums of A165872.
Sequence in context: A355899 A341050 A122506 * A010274 A137728 A054398
KEYWORD
sign
AUTHOR
STATUS
approved