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

1,2

Comments

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

Links

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

Example

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

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]

Crossrefs

The unitary version of A020492.

A078557 is a subsequence.

Cf. A034448, A047994, A335289.

Sequence in context: A146000 A134737 A030733 * A122839 A353869 A258077

Adjacent sequences: A335285 A335286 A335287 * A335289 A335290 A335291

Keyword

nonn

Author

Amiram Eldar, May 30 2020

Status

approved