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 A364975 #8 Apr 27 2025 00:45:12
%S A364975 12,30,42,88,120,140,186,534,678,6774,7962,77118,94108,152826,478194,
%T A364975 662154,935564,1128174,2028198,6934398,7750146,8330924,9984738,
%U A364975 10030804,22956114,62062566,151040622,284791602,732988732,804394974,1151476732,9040886574,31302713634
%N A364975 Admirable numbers (A111592) with a record gap to the next admirable number.
%C A364975 The corresponding record gaps are 8, 10, 12, 14, 18, 34, 36, 48, 84, 132, 204, 216, 254, 312, 348, 360, 392, 468, 516, 528, 552, 598, 624, 638, 828, 852, 936, 1056, 1082, 1128, 1454, 1692, 1752, ... .
%e A364975 The first 5 admirable numbers are 12, 20, 24, 30 and 40. The differences between these terms are 8, 4, 6 and 10. The record gaps, 8 and 10, occur after the terms 12 and 30, which are the first two terms of this sequence.
%t A364975 admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];
%t A364975 seq[kmax_] := Module[{s = {}, m = 12, dm = 0}, Do[If[admQ[k], d = k - m; If[d > dm, dm = d; AppendTo[s, m]]; m = k], {k, m + 1, kmax}]; s]; seq[10^6]
%o A364975 (PARI) isadm(n) = {my(ab=sigma(n)-2*n); ab>0 && ab%2 == 0 && ab/2 < n && n%(ab/2) == 0; }
%o A364975 lista(kmax) = {my(m = 12, dm = 0); for(k = m+1, kmax, if(isadm(k), d = k - m; if(d > dm, dm = d; print1(m, ", ")); m = k));}
%Y A364975 Cf. A111592, A364727.
%Y A364975 Similar sequences: A306953, A330870, A334418, A334419, A334883, A363296.
%K A364975 nonn
%O A364975 1,1
%A A364975 _Amiram Eldar_, Aug 15 2023