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 A194472 #71 Aug 05 2023 23:26:57
%S A194472 24,2016,8190,42336,45864,392448,714240,1571328,61900800,91963648,
%T A194472 211891200,1931236608,2013143040,4428914688,10200236032,214204956672
%N A194472 Erdős-Nicolas numbers.
%C A194472 Abundant numbers m such that the sum of the first k divisors is equal to m for some k, thus this is a subsequence of A064510. k has to be less than tau(m) - 1 for this sequence, whereas in A064510 k = tau(m) - 1 is allowed (and thus perfect numbers are in that sequence).
%C A194472 a(17) > 5*10^11. 104828758917120, 916858574438400, 967609154764800, 93076753068441600, 215131015678525440 and 1371332329173024768 are also terms. - _Donovan Johnson_, Dec 26 2012
%C A194472 a(17) > 10^12. - _Giovanni Resta_, Apr 15 2017
%C A194472 Equivalently, numbers whose abundancy equals 1 + the sum of the reciprocals of its first k divisors for some k > 1. - _Charlie Neder_, Feb 08 2019
%C A194472 96892692739248881664, 41407449045801454927872, 101616496263816777695232, 1346571992706422996646631651147776, 3304572752464376776401640967110656 are also terms. - _Michel Marcus_, Feb 09 2019
%C A194472 All known terms of A141643 (abundancy 5/2) are terms. - _Michel Marcus_, Feb 11 2019
%C A194472 Named after the Hungarian mathematician Paul Erdős (1913-1996) and the French mathematician Jean-Louis Nicolas. - _Amiram Eldar_, Jun 23 2021
%C A194472 Are all terms in this sequence even? - _Jenaro Tomaszewski_, May 07 2023
%D A194472 Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 141.
%H A194472 P. Erdős and J.-L. Nicolas, <a href="http://www.renyi.hu/~p_erdos/1975-37.pdf">Répartition des nombres superabondants</a>, Bull. Soc. Math. France, Vol. 103, No. 1 (1975), pp. 65-90.
%H A194472 Wikipedia, <a href="https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Nicolas_number">Erdős-Nicolas number</a>.
%e A194472 The divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24, hence 24 is in the list.
%e A194472 The divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The first seven of these add up to 36, but the first eight add up to 52, therefore 48 is not on the list.
%t A194472 subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[Divisors[n], -2]]; erdNickNums = {}; Do[If[selDivs[n] == 0, AppendTo[erdNickNums, n]], {n, 2, 10^5}]; erdNickNums (* Based on the program by Bobby R. Treat and _Robert G. Wilson v_ for A064510 *)
%o A194472 (PARI) isok(n) = {if (sigma(n) <= 2*n, return (0)); my(d = divisors(n), s = 0); for (k=1, #d-2, s += d[k]; if (s == n, return (1)); if (s > n, break);); return (0);} \\ _Michel Marcus_, Feb 09 2019
%o A194472 (Python)
%o A194472 from itertools import accumulate, count, islice
%o A194472 from sympy import divisors
%o A194472 def A194472_gen(startvalue=1): # generator of terms >= startvalue
%o A194472 return (n for n in count(max(startvalue,1)) if any(s == n for s in accumulate(divisors(n)[:-2])))
%o A194472 A194472_list = list(islice(A194472_gen(),5)) # _Chai Wah Wu_, Feb 18 2022
%Y A194472 Cf. A005835, A000396, A064510, A141643.
%K A194472 nonn,more
%O A194472 1,1
%A A194472 _Alonso del Arte_, Aug 24 2011
%E A194472 More terms from _M. F. Hasler_, Aug 24 2011