OFFSET
1,2
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.
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.
Wei Zhang, On a variant of the prime number theorem, Journal of Number Theory, Vol. 257 (2024), pp. 163-185; arXiv preprint, arXiv:2303.12347 [math.NT], 2023.
FORMULA
a(n) = c * n + O(n^(97/202 + eps)), for any eps > 0, where c = 1.695701... = A398531 (Bordellès, 2022).
The exponent in the error term was further improved to 9/19 + eps (Liu et al., 2024), and 107/229 + eps (Zhang, 2024).
MATHEMATICA
a[n_] := Sum[2^PrimeNu[Floor[n/k]], {k, 1, n}]; Array[a, 70]
PROG
(PARI) a(n) = sum(k = 1, n, 1 << omega(n\k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 01 2026
STATUS
approved
