A243455 Numbers n such that (n, sigma(n), tau(n)) lies on a sphere with integral radius centered at the origin, i.e., n^2 + sigma(n)^2 + tau(n)^2 is a square.

6, 61, 2089, 3606, 18585, 28710, 70981, 121374, 176529, 520320, 970783, 62788800, 114682878, 144653952, 174635334, 182054895, 3857228169, 4349012190, 15994971740, 17587660602, 22842677823, 65183331200, 66928439760

Offset: 1

Author

Michel Marcus, Jun 05 2014

Keywords

• nonn
• more

Comments

a(17) > 3*10^9. - Jinyuan Wang, Jul 09 2019

a(24) > 10^12, if it exists. - Giovanni Resta, Jul 17 2019

Examples

			6^2 + tau(6)^2 + sigma(6)^2 = 36 + 16 + 144 = 196 = 14^2. So 6 is in the sequence.
		

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A066764 (analog in 2d).

Programs

PARI

isok(n) = issquare(n^2 + numdiv(n)^2 + sigma(n)^2);

Extensions

a(13)-a(16) from Jinyuan Wang, Jul 09 2019

a(17)-a(23) from Giovanni Resta, Jul 17 2019