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

1,2

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

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.

Example

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.

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

Crossrefs

Cf. A002182, A067824, A307866, A333953.

Sequence in context: A140999 A168267 A308912 * A301414 A333953 A333963

Adjacent sequences: A333949 A333950 A333951 * A333953 A333954 A333955

Keyword

nonn

Author

Amiram Eldar, Apr 11 2020

Status

approved