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 A383697 #8 May 07 2025 10:50:33
%S A383697 900,1764,4356,4500,4900,6084,6300,8820,9900,10404,11700,12348,12996,
%T A383697 14700,15300,17100,19044,19404,20700,21780,22932,26100,27900,29988,
%U A383697 30276,30420,30492,31500,33300,33516,34596,36900,38700,40572,42300,42588,44100,47700,47916,49284,49500
%N A383697 Exponential squarefree exponential abundant numbers: numbers k such that A361174(k) > 2*k.
%C A383697 Subsequence of A383693 and first differs from it at n = 21.
%C A383697 All the terms are nonsquarefree numbers (A013929), since A361174(k) = k if k is a squarefree number (A005117).
%C A383697 The least odd term is a(198045) = 225450225, and the least term that is coprime to 6 is a(9.815...*10^17) = 1117347505588495206025.
%C A383697 The least term that is not an exponentially squarefree number (A209061) is a(8.85...*10^1324) = 2^4 * Product_{k=2..248} prime(k)^2 = 1.00786...*10^1328.
%C A383697 The asymptotic density of this sequence is Sum_{n>=1} f(A383698(n)) = 0.000878475..., where f(n) = (6/(Pi^2*n))*Product_{prime p|n}(p/(p+1)).
%H A383697 Amiram Eldar, <a href="/A383697/b383697.txt">Table of n, a(n) for n = 1..10000</a>
%t A383697 f[p_, e_] := DivisorSum[e, p^# &, SquareFreeQ[#] &]; q[k_] := Times @@ f @@@ FactorInteger[k] > 2*k; Select[Range[1000], q]
%o A383697 (PARI) ff(p, e) = sumdiv(e, d, if(issquarefree(d), p^d, 0));
%o A383697 isok(k) = {my(f = factor(k)); prod(i=1, #f~, ff(f[i, 1], f[i, 2])) > 2*k; }
%Y A383697 Subsequence of A013929, A129575 and A383693.
%Y A383697 A383698 is a subsequence.
%Y A383697 Cf. A005117, A209061, A361174.
%K A383697 nonn,easy
%O A383697 1,1
%A A383697 _Amiram Eldar_, May 06 2025