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 A109819 #18 Feb 05 2025 22:02:38
%S A109819 1,6,105,5005,37182145,6685349671,20496326086283047,
%T A109819 558516101711461766587,15322117939717490037614688353,
%U A109819 10978895066407230594062391177770267,150524069716274322800691458531160297587022319,4335344870389259769484516507207766258600144871515339
%N A109819 Product of primes between n and n^2.
%H A109819 Alois P. Heinz, <a href="/A109819/b109819.txt">Table of n, a(n) for n = 1..48</a>
%F A109819 log(a(n)) ~ n^2 by the Prime Number Theorem. - _Charles R Greathouse IV_, Feb 05 2025
%e A109819 a(3) = 105 because 3, 5 and 7 are the A073882(3) = 3 primes in the interval from 3 to 3^2 inclusive and 3 * 5 * 7 = 105.
%t A109819 Join[{1},Table[Product[Prime[i],{i,If[PrimeQ[n],PrimePi[n],PrimePi[n]+1],PrimePi[n^2]}],{n,2,10}]] (* _James C. McMahon_, Apr 01 2024 *)
%o A109819 (PARI) for(n=1,15,print1(prod(k=n,n^2,if(isprime(k),k,1)),","))
%Y A109819 Cf. A109818 (sum of same primes), A073882 (number of primes between n and n^2).
%K A109819 easy,nonn
%O A109819 1,2
%A A109819 _Rick L. Shepherd_, Jul 02 2005
%E A109819 More terms from _Michel Marcus_, Apr 02 2024