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

1,2

Comments

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

Links

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

Example

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.

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]

Crossrefs

Subsequence of A006086 and A103826.

Cf. A007340.

Sequence in context: A028244 A259817 A230842 * A000911 A076100 A353040

Adjacent sequences: A353036 A353037 A353038 * A353040 A353041 A353042

Keyword

nonn

Author

Amiram Eldar, Apr 19 2022

Status

approved