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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
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
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