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 A177442 #10 Apr 20 2023 04:22:15
%S A177442 2,6,15,22,55,68,85,145,261,296,333,370,492,533,590,885,944,1005,1143,
%T A177442 1207,1278,2831,2980,3048,3175,3302,3429,3576,3725,3874,4023,4775,
%U A177442 4966,7368,7582,7805,8289,8606,9036,9036,9287,9599,9599,9824,13902,14233
%N A177442 Smallest a(n) such that the prime factorization of a(n)! contains at least one factor to each exponent between 1 and n.
%H A177442 Amiram Eldar, <a href="/A177442/b177442.txt">Table of n, a(n) for n = 1..276</a>
%e A177442 15! = 2^11 * 3^6 * 5^3 * 7^2 * 11 * 13 and is the smallest number whose prime factorization has at least one factor with exponent 1, one factor with exponent 2, and one factor with exponent 3, so a(3)=15.
%t A177442 f[n_] := Module[{e = Union[FactorInteger[n!][[;; , 2]]]}, FirstPosition[Differences[e], _?(# > 1 &)][[1]]]; f[2] = f[3] = 1; seq[len_] := Module[{s = Table[0, {len}], n = 1, c = 0, i}, While[c < len, n++; i = f[n]; Do[If[s[[j]] == 0, c++; s[[j]] = n], {j, 1, Min[i, len]}]]; s]; seq[40] (* _Amiram Eldar_, Apr 20 2023 *)
%Y A177442 Cf. A000142.
%K A177442 nonn
%O A177442 1,1
%A A177442 _Jeff Burch_, May 08 2010
%E A177442 Corrected and extended by _D. S. McNeil_, May 22 2010