A295266 Positive integers whose squares can be represented as the sum or difference of 3-smooth numbers.

1, 2, 3, 5, 7, 17

Offset: 1

Author

Tomohiro Yamada, Nov 19 2017

Keywords

• nonn
• fini
• full

Comments

In Chapter 7 of de Weger's tract, it is shown that there are no other terms.

More generally, de Weger exposited how one can determine all squares which can be represented as the sum or difference of k-smooth numbers for any given k and determined all integers whose squares can be represented as the sum or difference of 7-smooth numbers, among which the largest one is 14117^2 = 199289869 = 3^13 * 5^3 - 2 * 7^3.

Examples

			a(6) = 17 ; 17^2 = 288 + 1 = 2^5 * 3^2 + 1.
		

Links

• B. M. M. de Weger, Algorithms for Diophantine Equations, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.

Crossrefs

Cf. A003586 (3-smooth numbers).

Coincides with A192579 and A215658 except the term 1.