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%I #8 Jan 04 2024 07:25:21
%S 2,3,2,2,4,2,2,3,2,3,2,5,2,3,2,2,4,2,2,2,3,3,2,2,6,2,3,2,2,4,4,2,3,2,
%T 2,5,2,2,2,3,3,4,2,2,3,2,2,3,2,7,2,3,3,2,4,2,2,2,3,2,2,5,4,2,3,2,2,2,
%U 2,4,2,3,2,3,6,2,2,3,2,2,4,2,3,2,5,2,2,3,2,2,4
%N The maximal exponent in the prime factorization of the nonsquarefree numbers.
%C The terms of A051903 that are larger than 1.
%H Amiram Eldar, <a href="/A368713/b368713.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A051903(A013929(n)).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (c * zeta(2) - 1)/(zeta(2) - 1) = 2.798673520766..., where c = 1.705211... is Niven's constant (A033150).
%t s[n_] := Max @@ Last /@ FactorInteger[n]; s /@ Select[Range[250], !SquareFreeQ[#] &]
%t (* or *)
%t f[n_] := Module[{e = Max @@ FactorInteger[n][[;; , 2]]}, If[e > 1, e, Nothing]]; Array[f, 250]
%o (PARI) lista(kmax) = {my(e); for(k = 2, kmax, e = vecmax(factor(k)[,2]); if(e > 1, print1(e, ", ")));}
%Y Cf. A013661, A013929, A033150, A051903.
%Y Similar sequences: A368710, A368711, A368712.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Jan 04 2024
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