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 A357695 #13 Aug 14 2025 05:38:18
%S A357695 12,18,20,30,36,42,60,66,70,78,84,90,100,102,114,126,132,138,140,150,
%T A357695 156,174,180,186,196,198,204,210,220,222,228,234,246,252,258,260,276,
%U A357695 282,294,300,306,308,318,330,340,342,348,350,354,364,366,372,380,390,396
%N A357695 Cubefree abundant numbers.
%C A357695 The least odd term is a(224) = A357697(1) = 1575.
%C A357695 The lower asymptotic density of this sequence is larger than 12/(91*zeta(3)) = 0.1097... which is the density of its subsequence of cubefree numbers larger than 6 and divisible by 6.
%C A357695 The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 13, 143, 1440, 14470, 144187, 1442500, 14426015, 144267400, 1442567879, 14425142573, ... . Apparently, the asymptotic density of this sequence exists and equals 0.1442... .
%H A357695 Amiram Eldar, <a href="/A357695/b357695.txt">Table of n, a(n) for n = 1..10000</a>
%e A357695 12 = 2^2 * 3 is a term since it is cubefree and sigma(12) = 28 > 2*12.
%t A357695 f[p_, e_] := (p^(e+1)-1)/(p-1); q[1] = False; q[n_] := AllTrue[(fct = FactorInteger[n])[[;;, 2]], # < 3 &] && Times @@ f @@@ fct > 2*n; Select[Range[400], q]
%o A357695 (PARI) is(n) = {my(f = factor(n)); (n==1 || vecmax(f[,2]) < 3) && sigma(f, -1) > 2};
%Y A357695 Intersection of A004709 and A005101.
%Y A357695 Subsequences: A087248, A357696, A357697.
%Y A357695 Cf. A000203 (sigma), A002117, A308618.
%K A357695 nonn
%O A357695 1,1
%A A357695 _Amiram Eldar_, Oct 10 2022