The Kravitz conjecture asserted that no positive integer has abundance equal to a positive odd
number that is a square number (Guy 2004). Write
,
where 
is the divisor function. 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).
The conjecture is false with smallest counterexample
 |  |  |
(1)
|
 |  |  |
(2)
|
and first few counterexamples given by 550564, 15038884, 57365476, ... (OEIS A188486).
