A333931 Recursive highly composite numbers: numbers with a record number of recursive divisors (A282446).

1, 2, 4, 6, 12, 30, 36, 60, 180, 420, 900, 1260, 4620, 6300, 13860, 44100, 55440, 69300, 180180, 485100, 720720, 900900, 2882880, 3063060, 6306300, 12252240, 15315300, 49008960, 58198140, 107207100, 232792560, 290990700, 931170240, 1163962800, 2036934900, 4655851200

Offset: 1

Author

Amiram Eldar, Apr 10 2020

Keywords

• nonn

Comments

The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 48, 54, ...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200

Crossrefs

Subsequence of A025487.

Cf. A282446.

Analogous sequences: A002182 (highly composite), A002110 (unitary), A037992 (infinitary), A293185 (bi-unitary), A309141 (nonunitary), A318278 (exponential).

Programs

Mathematica

recDivNum[1] = 1; recDivNum[n_] := recDivNum[n] = Times @@ (1 + recDivNum/@ (Last /@ FactorInteger[n])); rm = 0; s = {}; Do[r = recDivNum[n]; If[r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^4}]; s