A383921 Least integer k for which sigma(k - x) + sigma(k + x) >= n*k has at least one solution.

1, 2, 6, 24, 91, 841, 13861, 360361

Offset: 2

Author

Michel Marcus, May 15 2025

Keywords

• nonn
• more

Comments

The corresponding x are: 0, 0, 0, 0, 89, 839, 13859, 360359, ...

a(10) <= 61261201 via sigma(61261201 - 61261199) + sigma(61261201 + 61261199) >= 10*61261201. - David A. Corneth, May 16 2025

a(11) <= 20951330401 via sigma(20951330401 - 20951330399) + sigma(20951330401 + 20951330399) >= 11*20951330401. - Michel Marcus, May 22 2025

Crossrefs

Cf. A000203, A004394, A383758, A383920.

Programs

PARI

isok(k,n) = my(v=vector(k, x, (sigma(k - x + 1) + sigma(k + x - 1))/k)); my(vk = select(t->(t>=n), v, 1)); if (#vk != 0, v[1]);
a(n) = my(k=1); while (!isok(k, n), k++); k;

Extensions

a(9) from Jean-Marc Rebert, May 16 2025