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

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

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

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A392818. - Amiram Eldar, Jan 24 2026

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A006093, A023510, A051903, A392818.

Sequence in context: A097853 A160266 A322134 * A157905 A356718 A380203

Adjacent sequences: A023501 A023502 A023503 * A023505 A023506 A023507

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved