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

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

Offset: 1

Author

Amiram Eldar, Apr 19 2022

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

Cf. A006086, A034444, A335317.

Programs

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