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

Author

Amiram Eldar, Nov 19 2021

Keywords

• nonn

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A099377, A099378, A349473.

Programs

Mathematica

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