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 A387154 #15 Aug 20 2025 10:56:14
%S A387154 401120980260,360360,55440,110880,100800,120960,241920,483840,967680,
%T A387154 1935360,3870720,7741440,15482880,30965760,61931520,123863040,
%U A387154 247726080,495452160,990904320,1981808640,3963617280,7927234560,15854469120,31708938240,63417876480,126835752960
%N A387154 The least number k that is not n-free whose sum of n-free divisors is larger than 2*k.
%C A387154 n-free numbers are numbers that are not divisible by an n-th power larger than 1. E.g., A005117, A004709, and A046100 for n = 2, 3, and 4, respectively.
%C A387154 The sum of n-free divisors of a number is the sum of its divisors that are n-free numbers. E.g., A048250, A073185, and A385006 for n = 2, 3, and 4, respectively.
%C A387154 All the terms are in A025487.
%H A387154 Amiram Eldar, <a href="/A387154/b387154.txt">Table of n, a(n) for n = 2..1000</a>
%F A387154 a(n) = 945 * 2^n for n >= 7.
%e A387154 For n = 2, the numbers k such that A048250(k) > 2*k include all the squarefree abundant numbers (A087248). The least nonsquarefree number (A013929) k such that A048250(k) > 2*k is 401120980260 = 2^2*3*5*7*11*13*17*19*23*29*31.
%e A387154 For n = 3, the numbers k such that A073185(k) > 2*k include all the cubefree abundant numbers (A357695). The least noncubefree number (A046099) k such that A073185(k) > 2*k is A357700(1) = 360360 = 2^3*3^2*5*7*11*13.
%t A387154 a[n_] := If[n < 7, {401120980260, 360360, 55440, 110880, 100800}[[n-1]], 945 * 2^n]; Array[a, 26, 2]
%o A387154 (PARI) a(n) = if(n < 7, [401120980260, 360360, 55440, 110880, 100800][n-1], 945 * 2^n);
%Y A387154 Cf. A004709, A005117, A013929, A025487, A046099, A046100, A048250, A087248, A073185, A357695, A357700, A385006, A387155.
%K A387154 nonn,new
%O A387154 2,1
%A A387154 _Amiram Eldar_, Aug 19 2025