276, 552, 564, 660, 966
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On the 20th November 2021, I created a post titled 888 in which I mentioned one of the properties of that number being that it is on the trajectory of 552:
A014360 | Aliquot sequence starting at 552. |
The sequence begins:
552, 888, 1392, 2328, 3552, 6024, 9096, 13704, 20616, 30984
To quote from Wolfram Alpha:
It has not been proven that all aliquot sequences eventually terminate and become periodic. The smallest number whose fate is not known is 276. There are five such sequences less than 1000, namely 276, 552, 564, 660, and 966, sometimes called the "Lehmer five".
I was reminded of the Lehmer five again thanks to one of the properties associated with my diurnal age today (which is 27438):
A014363 | Aliquot sequence starting at 966. |
Figure 1: source |
A216072 | Aliquot open end sequences which belong to distinct families. |
These aliquot sequences are believed to grow forever without terminating in a prime or entering a cycle. Sequence A131884 lists all the starting values of an aliquot sequence that lead to open-ending. It includes all values obtained by iterating from the starting values of this sequence. But this sequence lists only the values that are the lowest starting elements of open end aliquot sequences that are the part of different open-ending families.V. Raman, Dec 08 2012