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 A356871 #9 Sep 03 2022 08:49:47
%S A356871 72,108,144,200,216,288,324,400,432,576,648,784,800,864,900,972,1000,
%T A356871 1152,1296,1568,1600,1728,1764,1800,1936,1944,2000,2304,2592,2700,
%U A356871 2704,2744,2916,3136,3200,3456,3528,3600,3872,3888,4000,4356,4500,4608,4900,5000,5184
%N A356871 Primitive coreful abundant numbers (second definition): coreful abundant numbers (A308053) that are powerful numbers (A001694).
%C A356871 For squarefree numbers k, csigma(k) = k, where csigma(k) is the sum of the coreful divisors of k (A057723). Thus, if m is a term (csigma(m) > 2*m) and k is a squarefree number coprime to k, then csigma(k*m) = csigma(k) * csigma(m) = k * csigma(m) > 2*k*m, so k*m is a coreful abundant number. Therefore, the sequence of coreful abundant numbers (A308053) can be generated from this sequence by multiplying with coprime squarefree numbers. The asymptotic density of the coreful abundant numbers can be calculated from this sequence (see comment in A308053).
%H A356871 Amiram Eldar, <a href="/A356871/b356871.txt">Table of n, a(n) for n = 1..10000</a>
%e A356871 72 is a term since csigma(72) = 168 > 2 * 72, and 72 = 2^3 * 3^2 is powerful.
%t A356871 f[p_, e_] := (p^(e+1)-1)/(p-1)-1; s[1] = 1; s[n_] := If[AllTrue[(fct = FactorInteger[n])[[;;, 2]], #>1 &], Times @@ f @@@ fct, 0]; seq={}; Do[If[s[n] > 2*n, AppendTo[seq, n]], {n, 1, 5000}]; seq
%Y A356871 Intersection of A001694 and A308053.
%Y A356871 A339940 is a subsequence.
%Y A356871 Cf. A057723.
%Y A356871 Similar sequences: A307959, A328136.
%K A356871 nonn
%O A356871 1,1
%A A356871 _Amiram Eldar_, Sep 02 2022