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%I #32 Jan 05 2024 02:55:40
%S 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,
%T 26,81,56,29,30,31,160,33,34,35,72,37,38,39,120,41,42,43,88,90,46,47,
%U 192,98,100,51,104,53,162,55,168,57,58,59,120,61,62,126,384
%N Highest exponent in the prime factorization of n^n.
%H Amiram Eldar, <a href="/A188385/b188385.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n * A051903(n). - _Franklin T. Adams-Watters_, Mar 29 2011
%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A033150 = 1.705211... . - _Amiram Eldar_, Jan 05 2024
%e For n = 1, 1^1 = 1, giving a(1) = 0.
%e For n = 12, 12^12 = 8916100448256 = (2^24)(3^12), giving a(12) = 24.
%t Join[{0}, Table[n*Max[Last /@ FactorInteger[n]], {n, 2, 100}]] (* _T. D. Noe_, Mar 30 2011 *)
%o (PARI) a(n) = if (n==1, 0, n*vecmax(factor(n)[,2])); \\ _Michel Marcus_, Dec 08 2020
%Y Cf. A000312, A033150, A051903.
%K nonn,easy
%O 1,2
%A _A. Timothy Royappa_, Mar 29 2011
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