A349688 Numbers k such that the sequence of elements of the continued fraction of the abundancy index of k is palindromic.

1, 6, 24, 28, 30, 42, 54, 66, 70, 78, 84, 90, 96, 102, 114, 120, 138, 140, 174, 186, 220, 222, 246, 258, 264, 270, 282, 308, 318, 330, 342, 348, 354, 364, 366, 402, 426, 438, 474, 476, 496, 498, 532, 534, 582, 606, 618, 642, 644, 654, 660, 672, 678, 744, 760, 762

Offset

1,2

Comments

All the multiply-perfect numbers (A007691) are terms of this sequence, since the continued fraction of their abundancy index contains a single element.

Links

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

Example

24 is a term since the sequence of elements of the abundancy index of 24, sigma(24)/24 = 5/2 = 2 + 1/2, is {2, 2}, which is palindromic.
42 is a term since the sequence of elements of the abundancy index of 42, sigma(42)/42 = 16/7 = 2 + 1/(3 + 1/2), is {2, 3, 2}, which is palindromic.

Mathematica

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

Prog

(PARI) isok(k) = my(v=contfrac(sigma(k)/k)); v == Vecrev(v); \\ Michel Marcus, Nov 25 2021

Crossrefs

Cf. A349685.

A007691 and A349686 are subsequences.

Similar sequence: A349477.

Sequence in context: A231324 A274557 A072710 * A273124 A349686 A069235

Adjacent sequences: A349685 A349686 A349687 * A349689 A349690 A349691

Keyword

nonn

Author

Amiram Eldar, Nov 25 2021

Status

approved