A055767 Index (or subscript) k of the largest primorial A002110(k) that divides the Euler phi of the n-th primorial (A005867(n)).

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, 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, 10, 10, 10, 10, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Labos Elemer, Jul 12 2000

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002110, A005867.

Programs

Mathematica

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 *)

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

Formula

a(n) = Max{k : primorial q(k) divides A000010(A002110(n))}.

Extensions

Data corrected by Sean A. Irvine, Apr 05 2022