A023504 Maximum exponent in the prime factorization of prime(n) - 1.

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, 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, 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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Examples

			The seventh prime is 17, and 16 = 2^4, so a(7) = 4.
The eighth prime is 19, and 18 = 2^1 * 3^2, and since 2 is the greater exponent, a(8) = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006093, A023510, A051903.

Programs

Mathematica

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

PARI

a(n) = if(n == 1, 0, vecmax(factor(prime(n) - 1)[, 2])); \\ Amiram Eldar, Sep 08 2024

Formula

a(n) = A051903(A006093(n)) . - R. J. Mathar, Feb 06 2019