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 A342091 #13 Sep 28 2022 03:48:54
%S A342091 1,2,4,6,10,15,22,33,44,55,68,85,102,119,145,174,203,232,261,296,333,
%T A342091 370,410,451,492,533,590,656,708,767,826,885,944,1005,1072,1143,1207,
%U A342091 1278,1422,1455,1562,1652,1778,1917,2032,2134,2235,2328,2425,2540,2682,2831,2929
%N A342091 a(n) is the least number k such that k! has n distinct exponents in its prime factorization.
%C A342091 After n=0, first differs from A073818 at n = 27.
%C A342091 a(n) is the least k such that A071625(k!) = A071626(k) = n.
%C A342091 Is this sequence strictly increasing?
%H A342091 Amiram Eldar, <a href="/A342091/b342091.txt">Table of n, a(n) for n = 0..2109</a> (terms below 10^7)
%H A342091 Paul Erdős, <a href="https://users.renyi.hu/~p_erdos/1982-08.pdf">Miscellaneous problems in number theory</a>, Proceedings of the Eleventh Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, Man., 1981), Congr. Numer., Vol. 34 (1982), pp. 25-45.
%e A342091 a(1) = 2 since 2! = 2^1 is the least factorial with a single exponent (1) in its prime factorization.
%e A342091 a(2) = 4 since 4! = 24 = 2^3 * 3^1 is the least factorial with 2 distinct exponents (1 and 3) in its prime factorization.
%e A342091 a(3) = 6 since 6! = 720 = 2^4 * 3^2 * 5^1 is the least factorial with 3 distinct exponents (1, 2 and 4) in its prime factorization.
%t A342091 f[1] = 0; f[n_] := Length @ Union[FactorInteger[n!][[;; , 2]]]; seq[max_] := Module[{s = Table[0, {max}], n = 1, c = 0}, While[c < max, i = f[n] + 1; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[50]
%Y A342091 Cf. A000142, A071625, A071626, A073818, A133924, A336616, A336619, A336867, A336868.
%K A342091 nonn
%O A342091 0,2
%A A342091 _Amiram Eldar_, Feb 27 2021