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 A250070 #66 Jun 20 2024 02:35:55
%S A250070 1,6,60,120,360,840,3360,2520,5040,10080,15120,32760,27720,50400,
%T A250070 98280,83160,110880,138600,221760,277200,332640,360360,554400,960960,
%U A250070 831600,942480,720720,2217600,1965600,1441440,3160080,2827440,2162160,2882880,3603600,5765760,5654880,4324320,9979200
%N A250070 Smallest number k such that the symmetric representation of sigma(k) has at least one part of width n.
%C A250070 The 26 entries starting with a(2) = 6 are products of powers of consecutive primes starting with 2, except for a(12) = 32760 and a(15) = 98280 (which are missing 11), and a(26) = 942480 (which is missing 13).
%C A250070 a(n) is the smallest number k such that the symmetric representation of sigma(k) has n layers. For more information see A279387. - _Omar E. Pol_, Dec 16 2016
%C A250070 Row 1 of A253258. - _Omar E. Pol_, Apr 15 2018
%C A250070 From _Hartmut F. W. Hoft_, Jun 10 2024: (Start)
%C A250070 All terms a(n) <= 1.75*10^7 have a symmetric representation of sigma that consists of a single part and they are abundant for n > 2. Numbers a(1) = 1, a(2) = 6, and a(4) = 120 are unimodal while numbers a(6) = 840, a(14) = 50400, a(18) = 138600, a(24) = 960960, a(26) = 942480, a(32) = 2827440, a(44) = 8648640 have a single extent of maximum width, but are not unimodal.
%C A250070 Conjecture: The symmetric representation of sigma for every term consists of a single part and it is unimodal only for a(1), a(2), and a(4).
%C A250070 As a consequence, this sequence would be a subsequence of A174973, and all a(n), n > 2, would be abundant. (End)
%H A250070 Hartmut F. W. Hoft, <a href="/A250070/b250070.txt">Table of n, a(n) for n = 1..48</a>
%F A250070 a(n) = min(k such that A250068(k) = n), n >= 1.
%e A250070 a(3) = 60 since the symmetric representation of sigma(60) = 168 consists of a single region of whose successive widths are 41 1's, 9 2's, 6 3's, 7 2's, 6 3's, 9 2's, and 41 1's.
%e A250070 a(6) = 840 has a single extent of 12 units of width 6 centered around point (583,583) on the diagonal, but is not unimodal. - _Hartmut F. W. Hoft_, Jun 10 2024
%t A250070 (* function a2[ ] is defined in A249223 *)
%t A250070 a250070[{j_, k_}, b_] := Module[{i, max, acc={{1, 1}}}, For[i=j, i<=k, i++, max={Max[a2[i]], i}; If[max[[1]]>b && !MemberQ[Transpose[acc][[1]], max[[1]]], AppendTo[acc,max]]]; acc]
%t A250070 (* returns (argument,result) data pairs since sequence is non-monotonic *)
%t A250070 Sort[a250070[{1, 1000000}, 1]] (* computed in steps *)
%Y A250070 Indices of records in A250068.
%Y A250070 Cf. A000203, A237270, A237271, A237593, A241008, A241010, A246955, A247687, A249223, A250071, A253258, A279387.
%Y A250070 Cf. A174973.
%K A250070 nonn
%O A250070 1,2
%A A250070 _Hartmut F. W. Hoft_, Nov 11 2014
%E A250070 a(28)-a(48) from _Hartmut F. W. Hoft_, Jun 10 2024