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%I #9 May 08 2024 08:53:02
%S 0,0,0,2,0,0,0,2,2,0,0,2,0,0,0,4,0,2,0,2,0,0,0,2,2,0,2,2,0,0,0,4,0,0,
%T 0,2,0,0,0,2,0,0,0,2,2,0,0,4,2,2,0,2,0,2,0,2,0,0,0,2,0,0,2,6,0,0,0,2,
%U 0,0,0,2,0,0,2,2,0,0,0,4,4,0,0,2,0,0,0
%N The maximal exponent in the prime factorization of the largest square dividing n.
%H Amiram Eldar, <a href="/A372602/b372602.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A051903(A008833(n)).
%F a(n) = A052928(A051903(n)).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 * Sum_{i>=1} (1 - (1/zeta(2*i))) = 0.98112786070359477197... .
%t f[n_] := 2 * Floor[n/2]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]
%o (PARI) s(n) = n \ 2 * 2;
%o a(n) = if(n>1, s(vecmax(factor(n)[,2])), 0);
%Y Cf. A008833, A051903, A052928.
%Y Similar sequences: A007424, A368781, A372601, A372603, A372604.
%K nonn,easy
%O 1,4
%A _Amiram Eldar_, May 07 2024