A220290 4-hyperperfect numbers: n = 4*(sigma(n)-n-1) + 1.

1950625, 1220640625, 186264514898681640625

Offset: 1

Author

Arkadiusz Wesolowski, Dec 11 2012

Keywords

• bref
• hard
• more
• nonn

Comments

For all k in A059613, (5^k-4)*5^(k-1) is a term. In particular, k=15 gives a term 186264514898681640625.

Links

• 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-A028502, A034916.

Programs

Mathematica

Select[Range[1, 2*10^6, 4], # + 3 == 4*(DivisorSigma[1, #] - #) &]

Extensions

a(3) from Max Alekseyev, Jun 01 2025