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a[n_] := Module[{dmax = 0}, Do[If[DivisorSigma[1, k] == n && (d = DivisorSigma[0, k]) > dmax, dmax = d], {k, 1, n}]; dmax]; Array[a, 100] (* Amiram Eldar, Apr 28 2021 *)
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Seiichi Manyama, <a href="/A341879/b341879.txt">Table of n, a(n) for n = 1..10000</a>
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k that satisfies sigma (k) = 12 is 6 or 11. d(6) = 4 and d(11) = 2. So a(12) = 4.
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