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 A124144 #11 Mar 11 2024 04:18:05
%S A124144 144,216,576,784,961,1296,1728,1764,2304,2744,3136,3600,3844,4356,
%T A124144 5184,6084,7056,7776,8100,9216,11664,12544,13824,14400,15376,15876,
%U A124144 17424,19600,20736,21952,24336,27000,28224,32400,34596,36864,38416,39204,41616,44100,46656,50176
%N A124144 Perfect powers pp such that sigma(k) = pp for some abundant number k.
%H A124144 Amiram Eldar, <a href="/A124144/b124144.txt">Table of n, a(n) for n = 1..10000</a>
%e A124144 a(1) = 144 since sigma(66) = 144 > 2*66 = 132.
%p A124144 with(numtheory); egcd := proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z->z[2],L); return igcd(op(L)) else return 1 fi; end; L:=[]: P:={}: for w to 1 do for n from 1 to 10000 do s:=sigma(n); if s>2*n and egcd(s)>1 then print(n,s,ifactor(s)); L:=[op(L),n]; P:=P union {s}; fi od od; L; P;
%t A124144 ppQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1;
%t A124144 f[n_] := Module[{s = DivisorSigma[1, n]}, If[s > 2*n, s, Nothing]];
%t A124144 seq[max_] := Union[Select[Array[f, max], # < max && ppQ[#] &]]; seq[60000] (* _Amiram Eldar_, Mar 11 2024 *)
%Y A124144 Cf. A001597, A005101, A065496.
%K A124144 nonn
%O A124144 1,1
%A A124144 _Walter Kehowski_, Dec 01 2006
%E A124144 a(32) inserted and more terms added by _Amiram Eldar_, Mar 11 2024