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

1,1

Comments

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

Links

Table of n, a(n) for n=1..14.

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.

Crossrefs

Sequence in context: A103590 A081699 A120570 * A336772 A098113 A172415

Adjacent sequences: A164011 A164012 A164013 * A164015 A164016 A164017

Keyword

nonn,more

Author

Charles R Greathouse IV, Jul 26 2011

Extensions

Definition corrected by Max Alekseyev, Nov 13 2012

Status

approved