A382504 Numbers k such that one or both of sigma(k) + k and sigma(k) - k is a perfect number.

6, 10, 25, 28, 496, 652, 8128, 10682, 10828, 33550336, 44655764, 8589869056, 8623554304

Offset: 1

Author

Leo Hennig, Mar 29 2025

Keywords

• nonn
• more

Comments

10 and 838476969534191044 are the only known numbers k for which sigma(k) + k is a perfect number.

Examples

			sigma(6) = 12 and 12 - 6 = 6.
sigma(10) = 18 and 18 + 10 = 28.
sigma(25) = 31 and 31 - 25 = 6.
		

Links

• Leo Hennig, One entry and just one entry, Seqfan thread.

Crossrefs

Supersequence of A000396 and of A237286.

Cf. A000203.

Programs

PARI

isp(x) = if (x>0, sigma(x) == 2*x);
isok(x) = isp(sigma(x)-x) || isp(sigma(x)+x); \\ Michel Marcus, Mar 29 2025