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 A055767 #19 Nov 13 2024 17:22:22
%S A055767 0,1,1,2,3,3,3,3,3,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,
%T A055767 7,7,7,7,7,7,7,7,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
%U A055767 10,10,10,10,16,16,16,16,16,16,16,16,16,16,16,16,16
%N A055767 Index (or subscript) k of the largest primorial A002110(k) that divides the Euler phi of the n-th primorial (A005867(n)).
%H A055767 Amiram Eldar, <a href="/A055767/b055767.txt">Table of n, a(n) for n = 1..10000</a>
%F A055767 a(n) = Max{k : primorial q(k) divides A000010(A002110(n))}.
%e A055767 For n = 52: the prime factors of phi(A002110(52)) = phi(2*3*5*7*...*233*239) are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 53, 83, 89, 113} in which the length of the initial prime continuous part is 10, thus a(52) = 10.
%t A055767 a[n_] := Module[{e = Times @@ (Prime[Range[n]] - 1), p = 2, k = 0}, While[Divisible[e, p], k++; p = NextPrime[p]]; k]; Array[a, 100] (* _Amiram Eldar_, Nov 12 2024 *)
%o A055767 (PARI) a(n) = {my(e = prod(i = 1, n, prime(i)-1), p = 2, k = 0); while(!(e % p), k++; p = nextprime(p+1)); k;} \\ _Amiram Eldar_, Nov 12 2024
%Y A055767 Cf. A000010, A002110, A005867.
%K A055767 nonn
%O A055767 1,4
%A A055767 _Labos Elemer_, Jul 12 2000
%E A055767 Data corrected by _Sean A. Irvine_, Apr 05 2022