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 A109874 #19 Apr 02 2024 02:59:51
%S A109874 1,2,2,4,4,6,5,7,8,10,9,12,11,12,12,16,14,18,16,18,20,22,19,22,24,22,
%T A109874 23,28,26,30,25,30,32,30,36,36,36,36,40,40,36,42,40,39,44,46,40,45,44,
%U A109874 46,48,52,45,50,49,54,56,58,54
%N A109874 Largest exponent e such that n^e that divides A001142(n).
%C A109874 a(n) = n-1, if n is a prime. If n is composite, a(n) >= 2.
%C A109874 Conjectures: (1) If n is even and n = 2^r*m, m odd and >1, then a(n)= n-r-1. (2) If n = 2^r then a(n) = n-3. (3) If n is odd and composite then a(n) = n-2.
%C A109874 a(n) is the highest exponent e such that n^e divides Product_{k=0..n} binomial(n, k). - _Joerg Arndt_, Jun 04 2022
%p A109874 A001142 := proc(n) local k ; mul(k^(2*k-1-n),k=1..n) ; end: A109874 := proc(n) local a,k; a := A001142(n) ; k := 0 ; while a mod n = 0 and a > 1 do a := a/n ; k := k+1 ; od; RETURN(k) ; end: seq(A109874(n),n=2..60) ; # _R. J. Mathar_, Aug 15 2007
%t A109874 a[n_] := IntegerExponent[Product[Binomial[n, k], {k, 0, n}], n];
%t A109874 Table[a[n], {n, 2, 60}] (* _Jean-François Alcover_, Apr 02 2024 *)
%o A109874 (PARI) for(n=2,60,print1(valuation(prod(k=0,n,binomial(n,k)),n),", ")); \\ _Joerg Arndt_, Jun 04 2022
%Y A109874 Cf. A001142, A109873.
%K A109874 nonn
%O A109874 2,2
%A A109874 _Amarnath Murthy_, Jul 10 2005
%E A109874 Corrected and extended by _R. J. Mathar_, Aug 15 2007
%E A109874 Name corrected by _Joerg Arndt_, Jun 04 2022