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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 (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

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Last modified October 26 04:27 EDT 2021. Contains 348256 sequences. (Running on oeis4.)