

A188486


Numbers k such that abundance(k) is an odd square.


4



550564, 15038884, 57365476, 197686728, 257859364, 1027291978962, 4644774970276, 319916794343524, 694453849937352, 97695446432293264, 359108743507594276, 25158930569552222884, 39753480499724798884, 58696020670745146276, 1021872661864058163600, 1397225158602002109604
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Counterexamples to the Kravitz conjecture. Subsequence of A188484 with positive abundances. Abundances are A188488, sigma(k)  2*k.
25158930569552222884 (found by Graeme Cohen) and 982150970230395945697746806666183824 (found by Sidney Kravitz) are also terms.  Amiram Eldar, May 17 2020


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B10, p. 74.


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..20 (terms < 10^26)
Eric Weisstein's World of Mathematics, Kravitz Conjecture


CROSSREFS

Cf. A033880, A188484, A188488.
Sequence in context: A337054 A337100 A077456 * A204571 A253614 A249687
Adjacent sequences: A188483 A188484 A188485 * A188487 A188488 A188489


KEYWORD

nonn,hard


AUTHOR

Eric W. Weisstein, Apr 01 2011


EXTENSIONS

a(4)a(5) from D. S. McNeil, Apr 02 2011
a(6)a(8) from Jack Brennen, May 03 2011
a(9) from Jack Brennen and Charles R Greathouse IV, May 04 2011
a(10)a(11) from Charles R Greathouse IV, May 04, 2011
Terms a(12) and beyond from Giovanni Resta, May 17 2020


STATUS

approved



