A028500 12-hyperperfect numbers: n = 12*(sigma(n) - n - 1) + 1.

697, 2041, 1570153, 62722153, 10604156641, 13544168521, 1792155938521

Offset: 1

Author

Jud McCranie

Keywords

• hard
• more
• nonn

Comments

7056410014866537089009269921 is also a term. - Donovan Johnson, Nov 20 2012

Also terms: 13^7*815787979*11621986347871 and 13^23*542800770374370512771595349. - Giovanni Resta, Nov 18 2019

a(8) >= 10^17. - Max Alekseyev, Nov 22 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, A028499, A028501, A028502, A034916, A220290.

Programs

PARI

isok(n) = 12*(sigma(n) - n - 1) + 1 == n; \\ Michel Marcus, Nov 18 2019

Extensions

a(7) from Donovan Johnson, Nov 20 2012