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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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

• Donovan Johnson, 2252 terms > 9*10^11
• Eric Weisstein's World of Mathematics, Fermat's Divisor Problem.

Crossrefs

Cf. A008849.

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