A385402 Numbers m >= 1 such that Sum_{k = 1..m} gcd(m, floor(m / k)) = Sum_{k = 1..m} gcd(m, ceiling(m / k)).

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 95, 97, 101, 103, 107, 109, 113, 119, 125, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 209, 211, 221

Offset: 1

Author

Ctibor O. Zizka, Jun 27 2025

Keywords

• nonn

Comments

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.

Examples

			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.
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.
		

Crossrefs

Cf. A018804, A384628, A385398.

Programs

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