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 A376331 #4 Sep 23 2024 13:37:09
%S A376331 6,105,257557397,362469273063260281,15119658537284521518782249,
%T A376331 117383204057701408834470517376101793436427,
%U A376331 23238824136447515117641387686174787861885627837847997511,139957288120766060385660710153537529132218663535147563443966068820553
%N A376331 a(n) is the smallest product of n consecutive primes p_1..p_k, where only p_1 < m^(1/n).
%C A376331 Proper subset of A120944, since squarefree m is the smallest number in the sequence of numbers that have m as squarefree kernel, and since more than 1 prime is a factor.
%F A376331 A374873(n) = lpf(a(n)) = A020639(a(n)).
%F A376331 a(n) = Product_{k=0..n-1} k + pi(A374873(n)), where pi = A000720.
%e A376331 a(2) = 6 since m = 2*3 = 6 and 3 > sqrt(6).
%e A376331 a(3) = 105 since m = 3*5*7 = 105 and 5 > 105^(1/3).
%e A376331 a(4) = 257557397 since m = 113 * 127 * 131 * 137 = 257557397 and 127 > 257557397^(1/4), etc.
%t A376331 k = 1; Table[r = Range[0, n - 1]; While[(Set[{p, q, m}, {#[[1]], #[[2]], Times @@ #}]; q < Surd[m, n]) &[Prime[k + r]], k++]; m, {n, 2, 6}]
%Y A376331 Cf. A120944, A374873, A375008, A375975, A376261.
%K A376331 nonn,hard
%O A376331 2,1
%A A376331 _Michael De Vlieger_, Sep 20 2024