login
Maximum exponent in the prime factorization of prime(n) - 1.
1

%I #20 Sep 08 2024 22:33:19

%S 0,1,2,1,1,2,4,2,1,2,1,2,3,1,1,2,1,2,1,1,3,1,1,3,5,2,1,1,3,4,2,1,3,1,

%T 2,2,2,4,1,2,1,2,1,6,2,2,1,1,1,2,3,1,4,3,8,1,2,3,2,3,1,2,2,1,3,2,1,4,

%U 1,2,5,1,1,2,3,1,2,2,4,3,1,2,1,4,1,1,6,3,2,1,1,1,5,2,1,1,2,3,2

%N Maximum exponent in the prime factorization of prime(n) - 1.

%H Harvey P. Dale, <a href="/A023504/b023504.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A051903(A006093(n)) . - _R. J. Mathar_, Feb 06 2019

%e The seventh prime is 17, and 16 = 2^4, so a(7) = 4.

%e The eighth prime is 19, and 18 = 2^1 * 3^2, and since 2 is the greater exponent, a(8) = 2.

%t Join[{0}, Max[FactorInteger[#][[All, 2]]]&/@(Prime[Range[2, 120]] - 1)] (* _Harvey P. Dale_, Aug 29 2017 *)

%o (PARI) a(n) = if(n == 1, 0, vecmax(factor(prime(n) - 1)[, 2])); \\ _Amiram Eldar_, Sep 08 2024

%Y Cf. A006093, A023510, A051903.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_