A317476 Harmonic numbers k such that the harmonic mean of the divisors of k is also a harmonic number.

1, 270, 164989440, 2701389600, 71271827200, 183694492800, 7322605472000, 28103080287744

Offset

1,2

Comments

The harmonic means of the divisors of the terms are 1, 6, 140, 270, 270, 672, 672, 496.

The terms 1, 2701389600 and 71271827200 have harmonic means of divisors which are also in this sequence.

Links

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

Example

270 is in the sequence since the harmonic mean of its divisors is 6, which is also a harmonic number.

Mathematica

hQ[n_] := IntegerQ[n*DivisorSigma[0, n]/DivisorSigma[1, n]]; hhQ[n_] :=  Module[{h = n * DivisorSigma[0, n]/DivisorSigma[1, n]}, IntegerQ[h] && hQ[h]]; Do[If[hhQ[n], Print[n]], {n, 1, 10^14}]

Crossrefs

Cf. A001599, A317477.

Sequence in context: A108094 A162007 A289136 * A290643 A104844 A086003

Adjacent sequences: A317473 A317474 A317475 * A317477 A317478 A317479

Keyword

nonn,more

Author

Amiram Eldar, Jul 29 2018

Status

approved