cp's OEIS Frontend

A103156 Numbers whose square can be expressed as the signed sum of a fifth power and a cube: z^2 = x^5 + y^3 with gcd(x,y,z)=1.

%I A103156 #13 Jul 08 2023 18:30:55
%S A103156 3,10,411,654,7792,36599,39151,647992,1506463,1525899,2730128,3353687,
%T A103156 4387861,4942947,5574720,12092581,128301258,168454745,184589480,
%U A103156 888155653,20364997771,53242416249,65464918703,73699708330,74330984303
%N A103156 Numbers whose square can be expressed as the signed sum of a fifth power and a cube: z^2 = x^5 + y^3 with gcd(x,y,z)=1.
%H A103156 Dario Alpern, <a href="https://www.alpertron.com.ar/SPOW532.HTM">Sum of powers a^5 + b^3 = c^2.</a>
%H A103156 Johnny Edwards, <a href="https://doi.org/10.1515/crll.2004.043">A Complete Solution to X^2+Y^3+Z^5=0.</a> Journal für die reine und angewandte Mathematik (Crelle's Journal) 571, 213-236 (2004).
%e A103156 a(1)=3 because 1^5 + 2^3 = 3^2;
%e A103156 a(2)=10 because (-3)^5 + 7^3 = 10^2;
%e A103156 a(3)=411 because 10^5 + 41^3 = 411^2;
%e A103156 a(4)=654 because 19^5 + (-127)^3 = 654^2.
%Y A103156 Cf. A070065 positive integer solutions of x^2 + y^5 = z^3.
%K A103156 nonn
%O A103156 1,1
%A A103156 _Hugo Pfoertner_, Jan 25 2005