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A353038
Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826).
0
90, 40682250, 81364500, 105773850, 423095400, 1798155450, 14385243600
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
The unitary version of A046999.
Subsequence of A006086.
Sequence in context: A135428 A028672 A172650 * A252093 A172756 A306304
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 19 2022
STATUS
approved