Friendly Number

A friendly number is a number that is a member of a friendly pair or a higher-order friendly n-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).

Friendly numbers have a positive density.

See also

Amicable Pair, Friendly Pair, Solitary Number

Explore with Wolfram|Alpha


Anderson, C. W. and Hickerson, D. Problem 6020. "Friendly Integers." Amer. Math. Monthly 84, 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]." 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 Number

Cite this as:

Weisstein, Eric W. "Friendly Number." From MathWorld--A Wolfram Web Resource.

Subject classifications