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4-hyperperfect numbers: n = 4*(sigma(n)-n-1) + 1.
7

%I #23 Nov 25 2019 08:58:12

%S 1950625,1220640625

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

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

%C a(3) > 10^17. - _Max Alekseyev_, Nov 25 2019

%H Judson S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A Study of Hyperperfect Numbers</a>, Journal of Integer Sequences, Vol. 3 (2000), Article 00.1.3.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperperfectNumber.html">Hyperperfect Number</a>

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

%Y Cf. A000396, A007593, A028499-A028502, A034916.

%K bref,hard,more,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Dec 11 2012