A363875 Numbers k such that there is no odd number whose aliquot sequence contains k.

2, 28, 52, 88, 96, 120, 124, 146, 162, 188, 206, 208, 210, 216, 238, 246, 248, 250, 262, 268, 276, 288, 290, 292, 298, 304, 306, 322, 324, 326, 336, 342, 362, 372, 388, 396, 406, 408, 412, 426, 428, 430, 438, 448, 452, 472, 474, 478, 486, 494, 498, 508, 516

Offset: 1

Author

Jinyuan Wang, Jun 25 2023

Keywords

• nonn

Comments

k is in sequence iff k can never be reached when iterating the map x -> A001065(x) starting with any odd number m.

Assuming the stronger version of Goldbach conjecture, iff k is in the sequence, there are infinitely many odd numbers whose aliquot sequence contain k.

Supersequence of A005114 (except 5), A283152, A284147, A284156, A284187, ..., and untouchable perfect numbers (28, 137438691328, ...), untouchable amicable numbers (A238382), untouchable sociable numbers.

Links

• Andrew R. Booker, Finite connected components of the aliquot graph, arXiv:1610.07471 [math.NT], 2017.
• Jean-Luc Garambois, Le graphe infini des suites aliquotes (in French).
• Wikipedia, Aliquot sequence

Crossrefs

Cf. A001065, A005114, A238382, A283152, A284147, A284156, A284187.