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 A342401 #10 Mar 11 2021 04:49:09
%S A342401 1,2,6,10,30,42,60,66,78,90,110,130,170,190,210,330,390,462,510,546,
%T A342401 570,690,798,858,870,930,1050,1110,1218,1230,1290,1410,1470,1554,1590,
%U A342401 1722,1770,1830,1974,2010,2130,2190,2310,2730,3570,3990,4290,4830,5610,6006
%N A342401 Numbers k such that the number of distinct sums of distinct unitary divisors of k sets a new record.
%C A342401 The corresponding record values are 1, 3, 12, 15, 72, 96, 108, 144, 168, 172, 183, 207, 231, 255, 576, 864, ... (see the link for more values).
%C A342401 The analogous sequence of records with all the divisors (A119347) is conjecturally the highly abundant numbers (A002093), excluding 3 and 10.
%H A342401 Amiram Eldar, <a href="/A342401/b342401.txt">Table of n, a(n) for n = 1..99</a>
%H A342401 Amiram Eldar, <a href="/A342401/a342401.txt">Table of n, a(n), A342400(a(n)) for n = 1..99</a>
%e A342401 The first 6 terms of A342400 are 1, 3, 3, 3, 3 and 12. The record values, 1, 3 and 12, occur are 1, 2 and 6, the first 3 terms of this sequence.
%t A342401 f[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], x, s, m, c}, m = Length[d]; s = Plus @@ d; c = Rest @ CoefficientList[Series[Product[1 + x^d[[i]], {i, 1, m}], {x, 0, s}], x]; Count[c, _?(# > 0 &)]]; fmax = -1; seq = {}; Do[f1 = f[n]; If[f1 > fmax, fmax = f1; AppendTo[seq, n]], {n, 1, 10^3}]; seq
%Y A342401 Cf. A002093, A119347, A342400.
%K A342401 nonn
%O A342401 1,2
%A A342401 _Amiram Eldar_, Mar 10 2021