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

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

Offset

1,1

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

Table of n, a(n) for n=1..7.

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

Prog

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

Crossrefs

Cf. A000396, A007593, A028499, A028501, A028502, A034916, A220290.

Sequence in context: A306097 A185377 A118059 * A133251 A243837 A116338

Adjacent sequences: A028497 A028498 A028499 * A028501 A028502 A028503

Keyword

hard,more,nonn

Author

Jud McCranie

Extensions

a(7) from Donovan Johnson, Nov 20 2012

Status

approved