Amenable Number

A number  is called amenable if it can be built up from integers , , ...,  by either addition or multiplication such that

(1)

(Tamvakis 1995).

The solutions are the numbers  such that  or 1 (mod 4), excluding  (Lossers 1998), giving 1, 5, 8, 9, 12, 13, 16, 17, ... (OEIS A100832). For example, 5 and 8 are amenable since

			(2)
			(3)
			(4)
			(5)

REFERENCES:

Lossers, O. P. "Solution to Problem 10454. Amenable Numbers." Amer. Math. Monthly 105, 1998.

Sloane, N. J. A. Sequence A100832 in "The On-Line Encyclopedia of Integer Sequences."

Tamvakis, H. "Problem 10454." Amer. Math. Monthly 102, 463, 1995.