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 A305616 #19 Dec 23 2024 09:54:13
%S A305616 15,63,147,171,207,627,663,1023,1647,1971,2975,6399,18063,19359,27639,
%T A305616 40215,48895,58563,78819,95511,114231,133595,134871,145915,147455,
%U A305616 163539,168507,172287,188067,529983,680859,795639,1207359,1238571,1553499,1588491,2049219
%N A305616 Near 2-hyperperfect numbers: numbers k such that sigma(k) - 3*k/2 - 1/2 is a proper divisor of k.
%C A305616 Supersequence of A063906.
%C A305616 A combination of the notions of 2-hyperperfect numbers (A007593) and near-perfect numbers (A181595).
%H A305616 Amiram Eldar, <a href="/A305616/b305616.txt">Table of n, a(n) for n = 1..70</a>
%H A305616 Bhabesh Das and Helen K. Saikia, <a href="https://vpcollege.org/wp-content/uploads/ijnt/volume_1/1.pdf">Identities for Near and Deficient Hyperperfect Numbers</a>, Indian Journal in Number Theory, Vol. 3 (2016), pp. 124-134.
%e A305616 15 is in the sequence since sigma(15) = 24 and 24 - 3*15/2 - 1/2 = 1 is a proper divisor of 15.
%t A305616 aQ[n_] := Module[{d=DivisorSigma[1, n]-3n/2-1/2}, d>0 && d!=n && IntegerQ[d] && Divisible[n,d]]; Select[Range[1000000], aQ]
%o A305616 (PARI) isok(n) = (n % 2) && (k = sigma(n) - (3*n+1)/2) && (k>0) && !(n % k) && (k != n); \\ _Michel Marcus_, Jun 07 2018
%Y A305616 Cf. A000203, A007593, A063906, A181595, A305617.
%K A305616 nonn
%O A305616 1,1
%A A305616 _Amiram Eldar_, Jun 06 2018