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%I #4 Nov 21 2017 20:03:08
%S 1,2,3,5,7,17
%N Positive integers whose squares can be represented as the sum or difference of 3-smooth numbers.
%C In Chapter 7 of de Weger's tract, it is shown that there are no other terms.
%C 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.
%H B. M. M. de Weger, <a href="https://www.win.tue.nl/~bdeweger/proefschrift.html">Algorithms for Diophantine Equations</a>, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.
%e a(6) = 17 ; 17^2 = 288 + 1 = 2^5 * 3^2 + 1.
%Y Cf. A003586 (3-smooth numbers).
%Y Coincides with A192579 and A215658 except the term 1.
%K nonn,fini,full
%O 1,2
%A _Tomohiro Yamada_, Nov 19 2017
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