A349502 Numbers k such that the continued fraction of the harmonic mean of the divisors of k contains distinct elements.

1, 2, 3, 6, 9, 14, 20, 24, 28, 32, 33, 35, 42, 44, 45, 51, 52, 55, 60, 65, 66, 68, 69, 70, 72, 84, 87, 88, 91, 95, 99, 104, 110, 114, 115, 117, 120, 123, 125, 126, 128, 135, 136, 138, 140, 141, 145, 152, 153, 156, 159, 170, 174, 177, 180, 182, 185, 186, 187, 188

Offset

1,2

Comments

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

Links

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

Example

2 is a term since the harmonic mean of the divisors of 2 is 4/3 = 1 + 1/3 and the elements of the continued fraction, {1, 3}, are different.
4 is not a term since the harmonic mean of the divisors of 4 is 12/7 = 1 + 1/(1 + 1/(2 + 1/2)) and the elements of the continued fraction, {1, 1, 2, 2}, are not distinct.

Mathematica

c[n_] := ContinuedFraction[DivisorSigma[0, n]/DivisorSigma[-1, n]]; q[n_] := Length[(cn = c[n])] == Length[DeleteDuplicates[cn]]; Select[Range[200], q]

Crossrefs

Cf. A001599, A349473, A349476.

Sequence in context: A061925 A073736 A101593 * A226893 A084628 A325269

Adjacent sequences: A349499 A349500 A349501 * A349503 A349504 A349505

Keyword

nonn

Author

Amiram Eldar, Nov 20 2021

Status

approved