A353039 Unitary arithmetic numbers k whose mean unitary divisor is a unitary divisor of k.

1, 6, 60, 420, 630, 5460, 8190, 16632, 64260, 143640, 172900, 598500, 716625, 790398, 791700, 1182384, 1187550, 1530144, 2708160, 4277448, 5314680, 6284250, 6397300, 6741630, 14619150, 15214500, 22144500, 24315984, 87966648, 93284100, 161670600, 165197760, 232517250

Offset: 1

Author

Amiram Eldar, Apr 19 2022

Keywords

• nonn

Comments

Also, unitary harmonic numbers k whose harmonic mean of the unitary divisors of k is a unitary divisor of k.

Examples

			6 is a term since the arithmetic mean of its unitary divisors, {1, 2, 3, 6}, is 3, and 3 is also a unitary divisor of 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..84

Crossrefs

Subsequence of A006086 and A103826.

Cf. A007340.

Programs

Mathematica

q[n_] := Module[{f = FactorInteger[n], d, s, m}, d = 2^Length[f]; s = Times @@ (1 + Power @@@ f); m = s/d; IntegerQ[m] && Divisible[n, m] && CoprimeQ[m, n/m]]; Select[Range[10^6], q]