A335831 Numbers k with a record value of tau(tau(k)) (A010553), where tau(k) is the number of divisors of k (A000005).

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

Amiram Eldar, Table of n, a(n) for n = 1..73

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.

Amiram Eldar, Table of n, a(n), A010553(a(n)) for n = 1..73

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.

Cf. A000005, A005179, A010553, A189394, A193987.

Sequence in context: A072487 A309875 A254232 * A189394 A182862 A072938

Adjacent sequences: A335828 A335829 A335830 * A335832 A335833 A335834

Keyword

nonn

Author

Amiram Eldar, Jun 25 2020

Status

approved