A008850 Numbers n such that sum of divisors of n^2 is a cube.

1, 43098, 20746664124, 21531558370, 25933330155, 30519275171, 453393100534, 803844998180, 1233758294601, 2358796315843, 6260406046762, 7339897643091, 7540242750903, 8532869860592, 11879890160946, 17538398093508

Offset

1,2

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 9.

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 54.

Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 92.

I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.

Links

Table of n, a(n) for n=1..16.

Donovan Johnson, 2252 terms > 9*10^11

Eric Weisstein's World of Mathematics, Fermat's Divisor Problem.

Crossrefs

Cf. A008849.

Sequence in context: A256950 A237847 A236984 * A205733 A205914 A205906

Adjacent sequences: A008847 A008848 A008849 * A008851 A008852 A008853

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson (whose search was complete only through a(2) = 43098), Sep 15 1996

Kaplansky gives two further numbers with this property: 2597942466059820 and 6847610254216117540. The first is probably new and the second is in Dickson.

I. Kaplansky and Will Jagy have verified that there are no other terms below 9*10^11. - Oct 13 2002

Status

approved