A335288 Unitary balanced numbers: numbers k such that uphi(k) (A047994) divides usigma(k) (A034448).

1, 2, 3, 6, 14, 15, 30, 35, 42, 44, 60, 70, 78, 105, 126, 132, 190, 210, 220, 312, 357, 418, 558, 570, 660, 693, 714, 728, 910, 1045, 1254, 1386, 1395, 1428, 1540, 2090, 2108, 2184, 2730, 2790, 3135, 3465, 3640, 3692, 3762, 4522, 4620, 4674, 5236, 5278, 6270

Offset: 1

Author

Amiram Eldar, May 30 2020

Keywords

• nonn

Comments

Terms that are also balanced numbers (A020492) include the squarefree balanced numbers (A078557). The nonsquarefree common terms are in A335289.

Examples

			6 is a term since usigma(6) = 12 is divisible by uphi(6) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The unitary version of A020492.

A078557 is a subsequence.

Cf. A034448, A047994, A335289.

Programs

Mathematica

f[1, 1] = 1; f[p_, e_]:= (p^e + 1)/(p^e -1); ubalQ[n_] := IntegerQ[Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^4], ubalQ]