A friendly number is a number that is a member of a friendly pair or a higher-order friendly -tuple. Numbers that are not friendly are said to be solitary.
There are some numbers that can easily be proved to be solitary,
but the status of numbers 10, 14, 15, 20, and many others remains unknown (Hickerson
2002). The numbers known to be friendly are given by 6, 12, 24, 28, 30, 40, 42, 56,
60, ... (OEIS A074902).
Anderson, C. W. and Hickerson, D. Problem 6020. "Friendly Integers." Amer. Math. Monthly84, 65-66, 1977.Sloane,
N. J. A. Sequences A050972, A050973,
and A074902 in "The On-Line Encyclopedia
of Integer Sequences."Hickerson, D. "Re: friendly/solitary
numbers [was: typos]." seqfan@ext.jussieu.fr. 19 Sep 2002. /archive/hickerson_2002-09-19.Pollack,
P. and Pomerance, C. "Some Problems of Erdős on the Sum-of-Divisors Function."
Trans. Amer. Math. Soc.3, 1-26, 2016.
-tuple. Numbers that are not friendly are said to be solitary.
There are some numbers that can easily be proved to be solitary,
but the status of numbers 10, 14, 15, 20, and many others remains unknown (Hickerson
2002). The numbers known to be friendly are given by 6, 12, 24, 28, 30, 40, 42, 56,
60, ... (OEIS A074902).
