This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385402 #6 Jul 02 2025 17:50:03
%S A385402 1,2,3,5,7,11,13,17,19,23,29,31,35,37,41,43,47,53,59,61,67,71,73,77,
%T A385402 79,83,89,95,97,101,103,107,109,113,119,125,127,131,137,139,143,149,
%U A385402 151,157,163,167,173,179,181,187,191,193,197,199,209,211,221
%N A385402 Numbers m >= 1 such that Sum_{k = 1..m} gcd(m, floor(m / k)) = Sum_{k = 1..m} gcd(m, ceiling(m / k)).
%C A385402 The list contains all primes p (A000040) because Sum_{k = 1..p} gcd(p, floor(p / k)) = 2*p - 1 and Sum_{k = 1..p} gcd(p, ceiling(p / k)) = 2*p - 1.
%e A385402 m = 5: Sum_{k = 1..5} gcd(5, floor(5 / k)) = 9, Sum_{k = 1..5} gcd(5, ceiling(5 / k)) = 9, 9 = 9, thus m = 5 is a term.
%e A385402 m = 35: Sum_{k = 1..35} gcd(35, floor(35 / k)) = 83, Sum_{k = 1..35} gcd(35, ceiling(35 / k)) = 83, 83 = 83, thus m = 35 is a term.
%o A385402 (PARI) isok(m) = sum(k=1, m, gcd(m, floor(m/k))) == sum(k=1, m, gcd(m, ceil(m/k))); \\ _Michel Marcus_, Jun 28 2025
%Y A385402 Cf. A018804, A384628, A385398.
%K A385402 nonn
%O A385402 1,2
%A A385402 _Ctibor O. Zizka_, Jun 27 2025