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 A383213 #20 Apr 26 2025 20:30:09
%S A383213 0,1,2,2,4,3,4,4,5,5,6,6,6,7,6,7,9,8,10,9,10,10,10,9,10,10,11,11,12,
%T A383213 13,12,12,14,14,14,14,14,14,16,14,16,15,16,17,16,17,18,17,18,18,18,18,
%U A383213 20,18,20,19,19,20,20,21,21,21,21,21,23,22,24,23,23,23
%N A383213 a(n) = number of distinct prime factors of binomial(2n,n+1).
%H A383213 Chai Wah Wu, <a href="/A383213/b383213.txt">Table of n, a(n) for n = 1..10000</a>
%e A383213 binomial(6,4)= 3*5, so a(3)=2.
%t A383213 Table[PrimeNu[Binomial[2 n, n + 1]], {n, 200}]
%o A383213 (PARI) a(n) = omega(binomial(2*n,n+1)); \\ _Michel Marcus_, Apr 19 2025
%o A383213 (Python)
%o A383213 from collections import Counter
%o A383213 from sympy import factorint
%o A383213 def A383213(n): return len(sum((Counter(factorint(i)) for i in range(n+2,(n<<1)+1)),start=Counter())-sum((Counter(factorint(i)) for i in range(1,n)),start=Counter())) # _Chai Wah Wu_, Apr 26 2025
%Y A383213 Cf. A000984, A001221, A067434, A383214.
%K A383213 nonn
%O A383213 1,3
%A A383213 _Clark Kimberling_, Apr 19 2025