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Table[Max[DivisorSigma[0, #] & /@ Range[n^2]], {n, 101}] (* Michael De Vlieger, Oct 11 2015 *)
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a(n) = Max( tau(k) : k=1,2,3,...,n*n ^2 ) where tau(k) = A000005(k) is the number of divisors of k.
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