A188385 Highest exponent in the prime factorization of n^n.

0, 2, 3, 8, 5, 6, 7, 24, 18, 10, 11, 24, 13, 14, 15, 64, 17, 36, 19, 40, 21, 22, 23, 72, 50, 26, 81, 56, 29, 30, 31, 160, 33, 34, 35, 72, 37, 38, 39, 120, 41, 42, 43, 88, 90, 46, 47, 192, 98, 100, 51, 104, 53, 162, 55, 168, 57, 58, 59, 120, 61, 62, 126, 384

Offset: 1

Author

A. Timothy Royappa, Mar 29 2011

Keywords

• nonn
• easy

Examples

			For n = 1, 1^1 = 1, giving a(1) = 0.
For n = 12, 12^12 = 8916100448256 = (2^24)(3^12), giving a(12) = 24.
		

Links

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

Crossrefs

Cf. A000312, A033150, A051903.

Programs

Mathematica

Join[{0}, Table[n*Max[Last /@ FactorInteger[n]], {n, 2, 100}]] (* T. D. Noe, Mar 30 2011 *)

PARI

a(n) = if (n==1, 0, n*vecmax(factor(n)[,2])); \\ Michel Marcus, Dec 08 2020

Formula

a(n) = n * A051903(n). - Franklin T. Adams-Watters, Mar 29 2011

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A033150 = 1.705211... . - Amiram Eldar, Jan 05 2024