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%I #16 Jun 26 2020 09:14:42
%S 1,2,6,12,60,360,1260,2520,5040,55440,277200,720720,3603600,61261200,
%T 129729600,908107200,2205403200,15437822400,293318625600,
%U 3226504881600,6746328388800,74209612276800,195643523275200,1855240306920000,2152078756027200,27977023828353600
%N Numbers k with a record value of tau(tau(k)) (A010553), where tau(k) is the number of divisors of k (A000005).
%C First differs from A189394 at n=15.
%C The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, ... (see the link for more values).
%H Amiram Eldar, <a href="/A335831/b335831.txt">Table of n, a(n) for n = 1..73</a>
%H Yvonne Buttkewitz, Christian Elsholtz, Kevin Ford and Jan-Christoph Schlage-Puchta, <a href="https://doi.org/10.1093/imrn/rnr175">A problem of Ramanujan, Erdős, and Kátai on the iterated divisor function</a>, International Mathematics Research Notices, Vol. 2012, No. 17 (2012), pp. 4051-4061, <a href="https://arxiv.org/abs/1108.1815">preprint</a>, arXiv:1108.1815 [math.NT], 2011.
%H Amiram Eldar, <a href="/A335831/a335831.txt">Table of n, a(n), A010553(a(n)) for n = 1..73</a>
%H Christian Elsholtz, Marc Technau and Niclas Technau, <a href="https://doi.org/10.1112/S0025579319000214">The maximal order of iterated multiplicative functions</a>, Mathematika, Vol. 65, No. 4 (2019), pp. 990-1009, <a href="https://arxiv.org/abs/1709.04799">preprint</a>, arXiv:1709.04799 [math.NT], 2017 and 2019.
%F tau(tau(a(n))) ~ c * sqrt(log(a(n)))/log(log(a(n))), where c is a constant (Buttkewitz et al., 2012).
%t f[n_] := DivisorSigma[0, DivisorSigma[0, n]]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 10^5}]; s
%Y Subsequence of A025487.
%Y Cf. A000005, A005179, A010553, A189394, A193987.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jun 25 2020
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