A074247 Numbers n such that harmonic mean of the divisors of n is a prime.

6, 28, 140, 496, 2970, 8128, 27846, 105664, 117800, 237510, 539400, 1421280, 1539720, 2290260, 4358600, 8872200, 33550336, 50401728, 90409410, 233103780, 287425800, 318177800, 423184320, 559903400, 825120800, 1632825792, 2705020500, 3209343200, 3328809120, 4720896180

Offset

1,1

Comments

Subsequence of A001599. Harmonic mean of divisors = n * tau(n) / sigma(n).

Links

Amiram Eldar, Table of n, a(n) for n = 1..103 (calculated from the b-file at A001599)

Example

140*tau(140)/sigma(140) = 5, a prime, so 140 is a term of the sequence.

Mathematica

Select[Range[10^5], PrimeQ[ # * DivisorSigma[0, # ] / DivisorSigma[1, # ]] &]
Select[Range[1600000], PrimeQ[HarmonicMean[Divisors[#]]]&] (* Harvey P. Dale, Jul 24 2019 *)

Crossrefs

Cf. A001599.

Sequence in context: A001599 A335316 A335317 * A053783 A216383 A283094

Adjacent sequences: A074244 A074245 A074246 * A074248 A074249 A074250

Keyword

nonn

Author

Joseph L. Pe, Sep 20 2002

Extensions

a(8)-a(26) from Donovan Johnson, Jun 10 2010

More terms from Amiram Eldar, Sep 30 2019

Status

approved