A164014 Numbers n for which the Hurwitz equation (x_1)^2 + (x_2)^2 + ... + (x_n)^2 = z * x_1 * x_2 * ... * x_n has solutions only for z = n.

12, 24, 32, 48, 60, 108, 240, 384, 480, 608, 972, 984, 1020, 2688

Offset: 1

Author

Charles R Greathouse IV, Jul 26 2011

Keywords

• nonn
• more

Comments

Conjectured finite. Any further terms are greater than 10^8.

Links

• A. Hurwitz, Über eine Aufgabe der unbestimmten Analysis, Archiv der Mathematik und Physik 11 (1907) pp. 185-196.
• Norman P. Herzberg, On a problem of Hurwitz, Pacific Journal of Mathematics 50 (1974), pp. 485-493.
• Ioulia Baoulina and Florian Luca, On positive integers with a certain nondivisibility property, Annales Mathematicae et Informaticae 35 (2008), pp. 11-19.

Extensions

Definition corrected by Max Alekseyev, Nov 13 2012