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 A330870 #7 Apr 29 2020 07:40:13
%S A330870 1,2,8,42,112,180,840,1600,6216,6272,16770,24240,29440,35910,184140,
%T A330870 197912,266112,319808,1321376,2003688,3121328,3696480,4017216,4543672,
%U A330870 5300910,5791302,11582680,12142088,27631300,31187592,31243040,64181800,106366560,307350504,1255812780
%N A330870 Practical numbers with a record gap to the next practical number.
%C A330870 The record gap values are 1, 2, 4, 6, 8, 12, 18, 20, 24, 28, 30, 36, 40, 42, 44, 48, 54, 64, 70, 72, 76, 80, 84, 88, 90, 98, 100, 112, 122, 124, 128, 136, 160, 180, 192, ...
%H A330870 Miriam Hausman and Harold N. Shapiro, <a href="https://doi.org/10.1002/cpa.3160370507">On practical numbers</a>, Communications on Pure and Applied Mathematics, Vol. 37, No. 5 (1984), pp. 705-713, section 4.
%H A330870 Giuseppe Melfi, <a href="http://www.seminariomatematico.polito.it/rendiconti/cartaceo/53-4/347.pdf">A survey on practical numbers</a>, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 53, No. 4 (1995), pp. 347-359, section 5.
%e A330870 The first 6 practical numbers are 1, 2, 4, 6, 8 and 12. The differences between these terms are 1, 2, 2, 2 and 4. The record gaps are 1, 2 and 4, which occur after the terms 1, 2 and 8.
%t A330870 f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[n_] := (ind = Position[(fct = FactorInteger[n])[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most @ fct]), _?(# > 1 &)]) == {}; seq = {}; m = 1; dm = 0; Do[If[pracQ[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 2, 10^6}]; seq
%Y A330870 Cf. A005153.
%Y A330870 Similar sequences: A306747, A306748, A306953.
%K A330870 nonn
%O A330870 1,2
%A A330870 _Amiram Eldar_, Apr 29 2020