A353040 Unitary harmonic numbers (A006086) with a record number of unitary divisors.

1, 6, 60, 420, 5460, 791700, 93284100, 3915147600, 285805774800

Offset

1,2

Comments

The corresponding record values are 1, 4, 8, 16, 32, 64, 128, 256, 512, ...

Links

Table of n, a(n) for n=1..9.

Example

The first 6 unitary harmonic numbers are 1, 6, 45, 60, 90, and 420. Their numbers of unitary divisors (A034444) are 1, 4, 4, 8, 8 and 16. The record values, 1, 4, 8 and 16 occur at 1, 6, 60 and 420, the first 4 terms of this sequence.

Mathematica

f[p_, e_] := 2 * p^e/(p^e + 1); r[n_] := Times @@ f @@@ FactorInteger[n]; dm = 0; s = {}; Do[h = r[n]; If[IntegerQ[h] && (d = 2^PrimeNu[n]) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s

Crossrefs

Cf. A006086, A034444, A335317.

Sequence in context: A353039 A000911 A076100 * A269760 A043033 A179711

Adjacent sequences: A353037 A353038 A353039 * A353041 A353042 A353043

Keyword

nonn,more

Author

Amiram Eldar, Apr 19 2022

Status

approved