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 A294197 #13 Jan 19 2025 12:00:34
%S A294197 3,8,27,120,650,4117,30380,255000,2402333,25086428,287582999
%N A294197 Floor of log base n! of product of all primes between n!+1 and (n+1)!.
%F A294197 a(n) = Sum_{i=primepi(n!)+1..primepi((n+1)!)} log(prime(i)) / log(n!).
%e A294197 a(3) = floor(log(7436429)/log(6)) = floor(8.830...) = 8.
%t A294197 Table[Floor[1/Log[n!] Plus @@ Table[Log[Prime[i]*1.], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}]], {n, 2, 10}]
%o A294197 (PARI) a(n) = floor(log(vecprod(primes([n!+1, (n+1)!])))/log(n!)); \\ _Michel Marcus_, Jan 19 2025
%Y A294197 Cf. A061232 (number of primes between n!+1 and (n+1)!).
%Y A294197 Cf. A294195 (product of primes between n!+1 and (n+1)!).
%Y A294197 Cf. A294196 (log of product of primes between n!+1 and (n+1)!).
%K A294197 nonn,more
%O A294197 2,1
%A A294197 _Olivier Gérard_, Oct 29 2017
%E A294197 a(12) from _Jinyuan Wang_, Jan 19 2025