A349476 Numbers k such that the continued fraction of the harmonic mean of the divisors of k contains a single distinct element.

1, 6, 15, 28, 30, 140, 270, 496, 545, 672, 792, 1365, 1638, 2970, 3515, 6200, 8128, 8190, 18600, 18620, 27846, 30240, 32760, 44950, 46359, 55860, 59670, 105664, 117800, 167400, 173600, 237510, 242060, 253539, 332640, 360360, 539400, 681156, 691782, 695520, 726180, 753480, 950976

Offset

1,2

Comments

All the harmonic numbers (A001599) are terms of this sequence.

The least term with m elements in the continued fraction of the harmonic mean of its divisors for m = 1, 2, 3, and 4 is 1, 15, 792 and 545, respectively.

Are there terms with more than 4 elements? There are no such terms below 2*10^9.

Links

Amiram Eldar, Table of n, a(n) for n = 1..150

Example

15 is a term since the harmonic mean of its divisors is 5/2 = 2 + 1/2.
545 is a term since the harmonic mean of its divisors is 109/33 = 3 + 1/(3 + 1/(3 + 1/3)).
792 is a term since the harmonic mean of its divisors is 528/65 = 8 + 1/(8 + 1/8).

Mathematica

c[n_] := ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; q[n_] := Length[Union[c[n]]] == 1; Select[Range[10^6], q]

Crossrefs

Cf. A099377, A099378, A349473.

Sequence in context: A333646 A063525 A335267 * A242454 A161777 A117519

Adjacent sequences: A349473 A349474 A349475 * A349477 A349478 A349479

Keyword

nonn

Author

Amiram Eldar, Nov 19 2021

Status

approved