A238382 Untouchable amicable numbers: amicable pairs which cannot be reached by any aliquot sequence starting from a number that does not belong to this pair.

356408, 399592, 643336, 652664, 5232010, 5799542, 9363584, 9437056, 10596368, 11199112, 15363832, 16517768, 31818952, 32205616, 34352624, 34860248, 46237730, 48641584, 48852176, 49215166, 52695376, 55349570, 56208368, 61319902, 91996816, 93259184

Offset: 1

Author

Jean Luc Garambois, Mar 03 2014

Keywords

• nonn

Comments

A pair of numbers x and y is called an untouchable amicable pair if x and y are amicable numbers (see A063990) and if x and y each have only one aliquot antecedent: the other number of their pair. In other words, they are amicable pairs which no aliquot sequence starting on a number that does not belong to this pair can reach.

The sequence lists the untouchable amicable numbers in increasing order. Note that the pairs x, y are not always adjacent to each other in the list.

Numbers that are the smaller number of their untouchable amicable pair are 356408, 643336, 5232010, 9363584, 10596368, 15363832, 31818952, 32205616, ... (subsequence of A002025).

The remaining numbers in the sequence are the larger number of their untouchable amicable pair: 399592, 652664, 5799542, 9437056, 11199112, 16517768, 34860248, 34352624, ... (subsequence of A002046).

We can call those pairs "untouchable amicable pairs", "isolated amicable pairs", or "isolated amicable cycles with two links" ... .

Links

• Jean-Luc Garambois, Aliquot sequences (in French, but with an English summary).
• Jean-Luc Garambois, Python program

Crossrefs

Cf. A063990, A048138, A001065.