A028499 6-hyperperfect numbers: n = 6*(sigma(n) - n - 1) + 1.

301, 16513, 60110701, 1977225901, 2733834545701, 232630479398401, 336823287227717101

Offset: 1

Author

Jud McCranie

Keywords

• hard
• more
• nonn

Comments

(7^k-6)*7^(k-1) is a term for all k in A191469. - Max Alekseyev, Nov 17 2019

Links

• Antal Bege, Kinga Fogarasi, Generalized perfect numbers, Acta Univ. Sapientiae, Math., 1 (2009), 73-82.
• Judson S. McCranie, A Study of Hyperperfect Numbers, Journal of Integer Sequences, Vol. 3 (2000), Article 00.1.3.
• Eric Weisstein's World of Mathematics, Hyperperfect Number

Crossrefs

Cf. A000396, A007593, A028500, A028501, A028502, A034916, A220290.

Programs

PARI

isok(n) = 6*(sigma(n) - n - 1) + 1 == n; \\ Michel Marcus, Nov 18 2019

Extensions

a(5) from Donovan Johnson, Nov 20 2012

a(6) from Donovan Johnson confirmed by Max Alekseyev, Nov 17 2019

a(7) from Giovanni Resta confirmed by Max Alekseyev, May 23 2025