A317477 Unitary harmonic numbers m such that the harmonic mean of the unitary divisors of m is also a unitary harmonic number.

1, 1512, 624937680, 808742880, 87348127500, 139103775360, 150780265560, 261880857000

Offset

1,2

Comments

The harmonic means of the unitary divisors of the terms are 1, 6, 45, 45, 45, 90, 45, 90.

Links

Table of n, a(n) for n=1..8.

Example

1512 is in the sequence since the harmonic mean of its divisors is 6 and 6 is also a unitary harmonic number.

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; ud[n_] := 2^PrimeNu[n]; uhQ[n_] := IntegerQ[n*ud[n]/usigma[n]]; uhuhQ[n_] :=  Module[{m = n*ud[n]/usigma[n]}, IntegerQ[m] && uhQ[m]]; Do[If[uhuhQ[n], Print[n]], {n, 1, 10^11}]

Crossrefs

Cf. A006086, A317476.

Sequence in context: A107523 A282253 A368545 * A064584 A318713 A252508

Adjacent sequences: A317474 A317475 A317476 * A317478 A317479 A317480

Keyword

nonn,more

Author

Amiram Eldar, Jul 29 2018

Status

approved