A333952 Recursively highly composite numbers: numbers m such that A067824(m) > A067824(k) for all k < m.

1, 2, 4, 6, 8, 12, 24, 36, 48, 72, 96, 120, 144, 192, 240, 288, 360, 432, 480, 576, 720, 864, 960, 1152, 1440, 1728, 1920, 2160, 2304, 2880, 3456, 4320, 5760, 6912, 8640, 11520, 17280, 23040, 25920, 30240, 34560, 46080, 51840, 60480, 69120, 86400, 103680, 120960

Offset: 1

Author

Amiram Eldar, Apr 11 2020

Keywords

• nonn

Comments

This sequence is not to be confused with A333931.

The corresponding record values are 1, 2, 4, 6, 8, 16, 40, 52, 96, ...

Fink (2019) defined this sequence. He asked whether 720 is the largest term that is also highly composite number (A002182).

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

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..291 (first 120 terms from Amiram Eldar)
• Thomas Fink, Recursively divisible numbers, arXiv:1912.07979 [math.NT], 2019. See section 5.
• T. M. A. Fink, Number of ordered factorizations and recursive divisors, arXiv:2307.16691 [math.NT], 2023.

Crossrefs

Cf. A002182, A067824, A307866, A333953.

Programs

Mathematica

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