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

1,1

Comments

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

Links

Table of n, a(n) for n=1..13.

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

Example

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

Prog

(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

Crossrefs

Supersequence of A000396 and of A237286.

Cf. A000203.

Sequence in context: A378362 A109095 A349692 * A351446 A323107 A077621

Adjacent sequences: A382501 A382502 A382503 * A382505 A382506 A382507

Keyword

nonn,more

Author

Leo Hennig, Mar 29 2025

Status

approved