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Friendly Number
A friendly number is a number that is a member of afriendly pair or a higher-order friendly
-tuple. Numbers that are not friendly are said to besolitary. There are some numbers that can easily be proved to besolitary, 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, ... (OEISA074902).
Friendly numbers have a positive density.
See also
Amicable Pair,FriendlyPair,Solitary NumberExplore with Wolfram|Alpha
References
Anderson, C. W. and Hickerson, D. Problem 6020. "Friendly Integers."Amer. Math. Monthly84, 65-66, 1977.Sloane, N. J. A. SequencesA050972,A050973, andA074902 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.Referenced on Wolfram|Alpha
Friendly NumberCite this as:
Weisstein, Eric W. "Friendly Number."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/FriendlyNumber.html