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 A385863 #37 Aug 22 2025 17:38:51
%S A385863 2,3,4,5,6,7,8,8,9,10,10,11,12,12,13,13,14,15,15,16,16,17,17,18,19,19,
%T A385863 20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,
%U A385863 31,32,32,33,33,33,34,34,35,35,36,36,37,37,38,38,39,39,39,40
%N A385863 a(n) is the largest number of distinct prime factors a number with at most n digits can have.
%C A385863 Also the largest k such that primorial(k) < 10^n.
%C A385863 "at most" in name could also be "exactly" and it gives the same data.
%C A385863 a(n) is the number of distinct prime factors of A091800(n).
%H A385863 Paolo Xausa, <a href="/A385863/b385863.txt">Table of n, a(n) for n = 1..10000</a>
%F A385863 a(n) = A001221(A091800(n)).
%e A385863 a(5) = 6 as primorial(6) = 30030 < 10^5 < 510510 = primorial(6 + 1) = primorial(7).
%t A385863 Table[First[FirstPosition[#, _?(# > n &)]] - 1, {n, Last[#] - 1}] & [IntegerLength[FoldList[Times, Prime[Range[50]]]]] (* _Paolo Xausa_, Aug 20 2025 *)
%o A385863 (PARI) a(n) = my(ulim=10^n-1, pp=1, t=0); forprime(p=2, oo, pp*=p; if(pp > ulim, return(t)); t++)
%Y A385863 Cf. A001221, A002110, A002283, A067175, A091800, A387173.
%K A385863 nonn,easy,base,new
%O A385863 1,1
%A A385863 _David A. Corneth_, Aug 20 2025