A349477 Numbers k such that the sequence of elements of the continued fraction of the harmonic mean of the divisors of k is palindromic.

1, 6, 8, 10, 15, 16, 21, 28, 30, 39, 48, 56, 57, 64, 93, 111, 129, 140, 183, 184, 192, 195, 200, 201, 210, 219, 220, 237, 270, 291, 309, 327, 345, 381, 417, 453, 471, 489, 496, 543, 545, 574, 579, 597, 600, 633, 645, 669, 672, 687, 723, 765, 792, 795, 798, 813

Offset: 1

Author

Amiram Eldar, Nov 19 2021

Keywords

• nonn

Comments

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

Examples

			8 is a term since the sequence of elements of the continued fraction of the harmonic mean of the divisors of 8, 32/15 = 2 + 1/(7 + 1/2), is {2, 7, 2}, which is palindromic.
		

Links

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

Crossrefs

A001599 and A349476 are subsequences.

Cf. A099377, A099378, A349473.

Programs

Mathematica

q[n_] := PalindromeQ[ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]]; Select[Range[1000], q]