Kravitz Conjecture

The first few numbers whose abundance absolute values are odd squares (excluding the trivial cases of powers of 2) are 98, 2116, 4232, 49928, 80656, 140450, 550564, 729632, ... (OEIS A188484).

Kravitz conjectured that no numbers exist whose abundance is a (positive) odd square (Guy 2004). This conjecture is false with smallest counterexample

			(1)
			(2)

and first few counterexamples given by 550564, 15038884, 57365476, ... (OEIS A188486).

REFERENCES:

Guy, R. K. Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, 2004.

Sloane, N. J. A. Sequence A188484 and A188486 in "The On-Line Encyclopedia of Integer Sequences."