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A317476
Harmonic numbers k such that the harmonic mean of the divisors of k is also a harmonic number.
1
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.
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
Sequence in context: A108094 A162007 A289136 * A290643 A104844 A086003
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 29 2018
STATUS
approved