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 A318168 #41 Apr 18 2024 04:22:14
%S A318168 18,42,54,66,78,102,114,126,138,162,174,186,196,198,222,234,246,258,
%T A318168 282,294,306,318,342,354,366,378,402,414,426,438,462,474,486,498,522,
%U A318168 534,546,558,582,594,606,618,642,654,666,678,702,714,726,738,762,774,786
%N A318168 Reverse Erdős-Nicolas numbers: abundant numbers m such that the sum of the last k proper divisors of m is equal to m for some k.
%C A318168 Apparently most of the terms are sum of their 3 largest proper divisors and are included in A074837. Terms that are not there are 196, 812, 868, 1036, 1148, 1204, 1316, 1372, 1484, 1652, 1708, 1876, 1998, 2044, ...
%C A318168 The possible values of k seem to be rather sparse. Up to 2*10^10, such values are: 3 (minimal m = 18), 5 (196), 9 (15376), 13 (1032256), 15 (34155), 16 (20482), 17 (33345), 19 (8415), 21 (407715), 23 (1273725), 26 (89245784), 32 (479198624), 36 (125226568), 40 (12499150), 45 (5905148248), 46 (1375270384), 68 (13968326788), and 91 (159030135). - _Giovanni Resta_, Aug 21 2018
%C A318168 If 2^p - 1 is prime then ((2^p - 1)^n)*2^(p-1) is in the sequence for n > 1. - _Davide Rotondo_, Oct 02 2021
%C A318168 From _Mauro Fiorentini_, Jan 08 2024: (Start)
%C A318168 More generally, if n is an even perfect number, with odd prime factor p, all prime factors of m are greater than n, k >= 0 and p^k*m > 1, n*p^k*m is in the sequence.
%C A318168 Also, if n is in the sequence and all prime factors of m are greater than n, n*m is in the sequence (note that n is not necessarily a multiple of an even perfect number).
%C A318168 It follows that there are infinitely many odd terms in the sequence, that the asymptotic density of the sequence is greater than 0.073482 and that the difference between consecutive terms is at most 24. (End)
%C A318168 The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 0, 5, 68, 737, 7352, 73704, 737142, 7370307, 73699222, 737011233, 7370145824, ... . Apparently, the asymptotic density of this sequence exists and equals 0.073701... . - _Amiram Eldar_, Apr 18 2024
%H A318168 Amiram Eldar, <a href="/A318168/b318168.txt">Table of n, a(n) for n = 1..10000</a>
%e A318168 196 is in the sequence since its proper divisors are 1, 2, 4, 7, 14, 28, 49, 98, and 7 + 14 + 28 + 49 + 98 = 196.
%t A318168 subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Reverse[Rest[Most[Divisors[n]]]]]; s={}; Do[If[selDivs[n] == 0, AppendTo[s, n]], {n, 2, 1000}]; s
%o A318168 (PARI) isok(n) = {my(d = Vecrev(divisors(n))); if (vecsum(d) > 2*n, my(s = 0); for (i=2, #d, s += d[i]; if (s == n, return(n)););); return (0);} \\ _Michel Marcus_, Aug 21 2018
%Y A318168 Cf. A000043, A000668, A074837, A194472.
%K A318168 nonn
%O A318168 1,1
%A A318168 _Amiram Eldar_, Aug 20 2018