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Numbers n such that harmonic mean of the divisors of n is a prime.
2

%I #12 Sep 30 2019 04:23:13

%S 6,28,140,496,2970,8128,27846,105664,117800,237510,539400,1421280,

%T 1539720,2290260,4358600,8872200,33550336,50401728,90409410,233103780,

%U 287425800,318177800,423184320,559903400,825120800,1632825792,2705020500,3209343200,3328809120,4720896180

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

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

%H Amiram Eldar, <a href="/A074247/b074247.txt">Table of n, a(n) for n = 1..103</a> (calculated from the b-file at A001599)

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

%t Select[Range[10^5], PrimeQ[ # * DivisorSigma[0, # ] / DivisorSigma[1, # ]] &]

%t Select[Range[1600000],PrimeQ[HarmonicMean[Divisors[#]]]&] (* _Harvey P. Dale_, Jul 24 2019 *)

%Y Cf. A001599.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Sep 20 2002

%E a(8)-a(26) from _Donovan Johnson_, Jun 10 2010

%E More terms from _Amiram Eldar_, Sep 30 2019