OFFSET
1,4
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Olivier Bordellès, On certain sums of number theory, International Journal of Number Theory, Vol. 18, No. 9 (2022), pp. 2053-2074; arXiv preprint, arXiv:2009.05751 [math.NT], 2020.
Mihoub Bouderbala and Meselem Karras, On a sum involving the number of distinct prime factors function related to the integer part function, Notes on Number Theory and Discrete Mathematics, Vol. 26, No. 4 (2020), pp. 52-56.
Kui Liu, Jie Wu, and Zhishan Yang, On some sums involving the integral part function, International Journal of Number Theory, Vol. 20, No. 3 (2024), pp. 831-847; arXiv preprint, arXiv:2109.01382 [math.NT], 2021.
FORMULA
a(n) = c * n + O(n^(1/2)*log(n)), where c = 0.591845... = A398529 (Bouderbala and Karras, 2020).
The error term was further improved to O(n^(455/914 + eps)), for any eps > 0 (Bordellès, 2022), and O(n^(53/110 + eps)), for any eps > 0 (Liu et al., 2024).
MATHEMATICA
a[n_] := Sum[PrimeNu[Floor[n/k]], {k, 1, n}]; Array[a, 70]
PROG
(PARI) a(n) = sum(k = 1, n, omega(n\k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 01 2026
STATUS
approved
