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

Author

Amiram Eldar, Nov 20 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001599, A349473, A349476.

Programs

Mathematica

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