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 A063769 #25 Feb 16 2025 08:32:45
%S A063769 25,95,119,143,417,445,565,608,650,652,675,685,783,790,909,913
%N A063769 Aspiring numbers: numbers whose aliquot sequence terminates in a perfect number.
%C A063769 There are many numbers whose aliquot sequences have not yet been completely computed, so this sequence is not fully known. In particular, 276 may, perhaps, be an element of this sequence, although this is very unlikely.
%C A063769 Numbers less than 1000 whose aliquot sequence is not known that could possibly be in this sequence are: 276, 306, 396, 552, 564, 660, 696, 780, 828, 888, 966, 996. - _Robert Price_, Jun 03 2013
%D A063769 No number terminates at 28, the second perfect number.
%H A063769 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AspiringNumber.html">Aspiring Number</a>
%e A063769 The divisors of 95 less than itself are 1, 5 and 19. They sum to 25. The divisors of 25 less than itself are 1 and 5. They sum to 6, which is perfect.
%t A063769 perfectQ[n_] := DivisorSigma[1, n] == 2*n; maxAliquot = 10^45; A131884 = {}; s[1] = 1; s[n_] := DivisorSigma[1, n] - n; selQ[n_ /; n <= 5] = False; selQ[n_] := NestWhile[s, n, If[{##}[[-1]] > maxAliquot, Print["A131884: ", n]; AppendTo[A131884, n]; False, Length[{##}] < 4 || {##}[[-4 ;; -3]] != {##}[[-2 ;; -1]]] &, All] // perfectQ; Reap[For[k = 1, k < 1000, k++, If[! perfectQ[k] && selQ[k], Print[k]; Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Nov 15 2013 *)
%Y A063769 Cf. A080907, A115350.
%K A063769 hard,nice,nonn
%O A063769 1,1
%A A063769 _Tanya Khovanova_ and Alexey Radul, Aug 14 2001
%E A063769 a(13)-a(16) from _Robert Price_, Jun 03 2013