A377708 Numbers k that have a record number of divisors d such that gcd(d, k/d) is an exponentially odd number (A268335).

1, 2, 4, 6, 12, 24, 36, 60, 120, 180, 360, 840, 1260, 2520, 6300, 7560, 12600, 27720, 69300, 83160, 138600, 360360, 900900, 1081080, 1801800, 5405400, 12612600, 18378360, 30630600, 91891800, 214414200, 349188840, 581981400, 1745944200, 4073869800, 8031343320, 12221609400

Offset: 1

Author

Amiram Eldar, Nov 04 2024

Keywords

• nonn

Comments

First differs from A365681 at n = 22.

First differs from A377140 at n = 95.

Indices of records in A365173.

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..164
• Amiram Eldar, Table of n, a(n), A365173(a(n)) for n = 1..164

Crossrefs

Cf. A268335, A365173, A365681, A377140.

Subsequence of A025487.

Programs

Mathematica

f[p_, e_] := Floor[(e + 5)/4] + Floor[(e + 6)/4]; 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