A365681 Numbers with a record number of exponentially squarefree divisors.

1, 2, 4, 6, 12, 24, 36, 60, 120, 180, 360, 840, 1260, 2520, 6300, 7560, 12600, 27720, 69300, 83160, 138600, 332640, 360360, 900900, 1081080, 1801800, 4324320, 5405400, 12612600, 17297280, 18378360, 30630600, 73513440, 86486400, 91891800, 214414200, 294053760

Offset: 1

Author

Amiram Eldar, Sep 15 2023

Keywords

• nonn

Comments

Indices of records of A365680.

The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..255
• Amiram Eldar, Table of n, a(n), A365680(a(n)) for n = 1..255

Crossrefs

Cf. A365680.

Subsequence of A025487.

Similar sequences: A306736, A307845, A318278.

Programs

Mathematica

f[p_, e_] := Count[Range[e], ?SquareFreeQ] + 1; d[1] = 1; d[n] := Times @@ f @@@ FactorInteger[n]; v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq