This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038536 #22 May 26 2025 09:55:00
%S A038536 3,11,19,31,35,59,75,91,111,115,131,151,179,235,255,311,335,339,371,
%T A038536 375,399,411,431,439,495,515,531,539,551,591,619,675,739,791,795,811,
%U A038536 839,851,871,915,951,999,1015,1035,1039,1055,1071,1075,1155,1231,1351
%N A038536 Odd values of k > 1 for which there are k-hyperperfect numbers.
%C A038536 ((3*k+1)/2)^2*(3*k+4) is k-hyperperfect.
%D A038536 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B2, p. 79.
%D A038536 Joe Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 177.
%H A038536 Amiram Eldar, <a href="/A038536/b038536.txt">Table of n, a(n) for n = 1..10000</a>
%H A038536 Judson S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A study of hyperperfect numbers</a>, J. Int. Seq., Vol. 3 (2000), Article 00.1.3.
%H A038536 Daniel Minoli, <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0559206-9">Issues In Non-Linear Hyperperfect Numbers</a>, Mathematics of Computation, Vol. 34, No. 150, April 1980, pp. 639-645.
%t A038536 q[k_] := Module[{m = (3*k + 1)^2*(3*k + 4)/4}, Divisible[m - 1, DivisorSigma[1, m] - m - 1]]; Select[Range[3, 1500, 2], q] (* _Amiram Eldar_, May 25 2025 *)
%o A038536 (PARI) isok(k) = if(k == 1 || !(k % 2), 0, my(m = (3*k + 1)^2*(3*k + 4)/4); !((m-1) % (sigma(m)-m-1))); \\ _Amiram Eldar_, May 25 2025
%Y A038536 Cf. A007592.
%K A038536 nonn
%O A038536 1,1
%A A038536 _Jud McCranie_