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

1,4

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000010, A002110, A005867.

Sequence in context: A374942 A280455 A284725 * A029110 A249420 A103959

Adjacent sequences: A055764 A055765 A055766 * A055768 A055769 A055770

Keyword

nonn

Author

Labos Elemer, Jul 12 2000

Extensions

Data corrected by Sean A. Irvine, Apr 05 2022

Status

approved