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A335831
Numbers k with a record value of tau(tau(k)) (A010553), where tau(k) is the number of divisors of k (A000005).
2
1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600, 61261200, 129729600, 908107200, 2205403200, 15437822400, 293318625600, 3226504881600, 6746328388800, 74209612276800, 195643523275200, 1855240306920000, 2152078756027200, 27977023828353600
OFFSET
1,2
COMMENTS
First differs from A189394 at n=15.
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).
LINKS
Yvonne Buttkewitz, Christian Elsholtz, Kevin Ford and Jan-Christoph Schlage-Puchta, A problem of Ramanujan, Erdős, and Kátai on the iterated divisor function, International Mathematics Research Notices, Vol. 2012, No. 17 (2012), pp. 4051-4061, preprint, arXiv:1108.1815 [math.NT], 2011.
Christian Elsholtz, Marc Technau and Niclas Technau, The maximal order of iterated multiplicative functions, Mathematika, Vol. 65, No. 4 (2019), pp. 990-1009, preprint, arXiv:1709.04799 [math.NT], 2017 and 2019.
FORMULA
tau(tau(a(n))) ~ c * sqrt(log(a(n)))/log(log(a(n))), where c is a constant (Buttkewitz et al., 2012).
MATHEMATICA
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
CROSSREFS
Subsequence of A025487.
Sequence in context: A072487 A309875 A254232 * A189394 A182862 A072938
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 25 2020
STATUS
approved