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 A383390 #14 Apr 26 2025 13:25:42
%S A383390 104,495,584,735,944,1155,1364,1484,2144,2204,2415,2624,2924,2925,
%T A383390 3135,3255,3794,3795,4304,4484,4784,4844,5264,5355,5445,5564,5565,
%U A383390 5655,5775,5984,6104,6764,7424,7455,7664,7755,7875,8084,8294,8295,8414,8415,8924,9009,9344,9944,9975
%N A383390 Numbers k such that k^2 and (k+1)^2 are both abundant numbers.
%C A383390 The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 5, 47, 459, 4655, 46733, 460693, 4612685, 46177602, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00461... .
%H A383390 Amiram Eldar, <a href="/A383390/b383390.txt">Table of n, a(n) for n = 1..10000</a>
%t A383390 Select[Range[10000], DivisorSigma[-1, #^2] > 2 && DivisorSigma[-1, (#+1)^2] > 2 &]
%o A383390 (PARI) is1(k) = {my(f = factor(k)); prod(i = 1, #f~, f[i,2] *= 2); sigma(f, -1) > 2;}
%o A383390 list(lim) = {my(q1 = is1(1), q2); for(k = 2, lim, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}
%Y A383390 Subsequence of A381738.
%Y A383390 A383391 and A096399 are subsequences.
%Y A383390 Cf. A005101, A063734.
%K A383390 nonn
%O A383390 1,1
%A A383390 _Amiram Eldar_, Apr 25 2025