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%I #21 Aug 02 2023 07:20:10
%S 1,2,4,6,8,12,24,36,48,72,96,120,144,192,240,288,360,432,480,576,720,
%T 864,960,1152,1440,1728,1920,2160,2304,2880,3456,4320,5760,6912,8640,
%U 11520,17280,23040,25920,30240,34560,46080,51840,60480,69120,86400,103680,120960
%N Recursively highly composite numbers: numbers m such that A067824(m) > A067824(k) for all k < m.
%C This sequence is not to be confused with A333931.
%C The corresponding record values are 1, 2, 4, 6, 8, 16, 40, 52, 96, ...
%C Fink (2019) defined this sequence. He asked whether 720 is the largest term that is also highly composite number (A002182).
%C This is, except the terms 2, the sequence records of indices of A074206 for positive n as a(n) = 2*A074206(n), n>1, i.e. A307866. (formula from - Vladeta Jovovic, Jul 03 2005) - _David A. Corneth_, Apr 13 2020
%H David A. Corneth, <a href="/A333952/b333952.txt">Table of n, a(n) for n = 1..291</a> (first 120 terms from Amiram Eldar)
%H Thomas Fink, <a href="https://arxiv.org/abs/1912.07979">Recursively divisible numbers</a>, arXiv:1912.07979 [math.NT], 2019. See section 5.
%H T. M. A. Fink, <a href="https://arxiv.org/abs/2307.16691">Number of ordered factorizations and recursive divisors</a>, arXiv:2307.16691 [math.NT], 2023.
%e The first 6 terms of A067824 are 1, 2, 2, 4, 2, 6. The record values occur at 1, 2, 4, 6, the first 4 terms of this sequence.
%t d[1] = 1; d[n_] := d[n] = 1 + DivisorSum[n, d[#] &, # < n &]; seq={}; dm = 0; Do[d1 = d[n]; If[d1 > dm, dm = d1; AppendTo[seq, n]], {n, 1, 10^4}]; seq
%Y Cf. A002182, A067824, A307866, A333953.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 11 2020
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