%I #35 Feb 16 2025 08:33:14
%S 550564,15038884,57365476,197686728,257859364,1027291978962,
%T 4644774970276,319916794343524,694453849937352,97695446432293264,
%U 359108743507594276,25158930569552222884,39753480499724798884,58696020670745146276,1021872661864058163600,1397225158602002109604
%N Numbers k such that abundance(k) is an odd square.
%C Counterexamples to the Kravitz conjecture. Subsequence of A188484 with positive abundances. Abundances are A188488, sigma(k) - 2*k.
%C 25158930569552222884 (found by Graeme Cohen) and 982150970230395945697746806666183824 (found by Sidney Kravitz) are also terms. - _Amiram Eldar_, May 17 2020
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B10, p. 74.
%H Giovanni Resta, <a href="/A188486/b188486.txt">Table of n, a(n) for n = 1..20</a> (terms < 10^26)
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KravitzConjecture.html">Kravitz Conjecture</a>
%Y Cf. A033880, A188484, A188488.
%K nonn,hard,changed
%O 1,1
%A _Eric W. Weisstein_, Apr 01 2011
%E a(4)-a(5) from _D. S. McNeil_, Apr 02 2011
%E a(6)-a(8) from _Jack Brennen_, May 03 2011
%E a(9) from _Jack Brennen_ and _Charles R Greathouse IV_, May 04 2011
%E a(10)-a(11) from _Charles R Greathouse IV_, May 04, 2011
%E Terms a(12) and beyond from _Giovanni Resta_, May 17 2020