OFFSET
1,1
COMMENTS
There are 290 unitary harmonic numbers below 10^12, and only 7 of them are in this sequence.
EXAMPLE
90 is in the sequence since its unitary divisors are {1, 2, 5, 9, 10, 18, 45, 90}, their harmonic mean, 4, is an integer, but their arithmetic mean, 45/2, is not.
MATHEMATICA
q[n_] := Module[{f = FactorInteger[n], d, s}, d = 2^Length[f]; s = Times @@ (1 + Power @@@ f); IntegerQ[n*d/s] && !IntegerQ[s/d]]; Select[Range[5*10^7], q]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 19 2022
STATUS
approved