A353038 Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826).

90, 40682250, 81364500, 105773850, 423095400, 1798155450, 14385243600

Offset: 1

Author

Amiram Eldar, Apr 19 2022

Keywords

• nonn
• more

Comments

There are 290 unitary harmonic numbers below 10^12, and only 7 of them are in this sequence.

Examples

			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.
		

Crossrefs

The unitary version of A046999.

Subsequence of A006086.

Cf. A006087, A103826.

Programs

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]