A377707 Numbers k that have a record number of divisors d such that gcd(d, k/d) is a square.

1, 2, 6, 30, 210, 1680, 2310, 18480, 30030, 240240, 480480, 3843840, 4084080, 8168160, 65345280, 77597520, 155195040, 1241560320, 1784742960, 3569485920, 28555887360, 51757545840, 103515091680, 828120733440, 1604483921040, 3208967842080, 25671742736640, 51343485473280

Offset: 1

Author

Amiram Eldar, Nov 04 2024

Keywords

• nonn

Comments

Indices of records in A365171.

The corresponding record values are 1, 2, 4, 8, 16, 24, 32, 48, 64, 96, ... (see the link for more values).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..102
• Amiram Eldar, Table of n, a(n), A365171(a(n)) for n = 1..102

Crossrefs

Cf. A365171.

Subsequence of A025487.

Programs

Mathematica

f[p_, e_] := Floor[(e + 3)/4] + Floor[(e + 4)/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