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A087209 Numbers k such that k^2 = x^3 + y^4 with positive integers x, y. 1

%I #12 Jul 09 2023 00:02:06

%S 3,29,45,76,162,192,397,405,612,650,1025,1098,1275,1856,2064,2160,

%T 2187,2880,3420,4864,5499,6831,6875,8775,9072,10368,12288,12348,15000,

%U 21096,21141,25408,25920,26811,29079,30600,30758,32805,33957,36875,39168

%N Numbers k such that k^2 = x^3 + y^4 with positive integers x, y.

%C There are an infinite number of solutions. Parametrizations are given at the Alpern link.

%H Dario Alpern, <a href="https://www.alpertron.com.ar/SUMPOWER.HTM#4_3_2">Sum of powers</a>

%e 3 is a term because 3^2 = 2^3 + 1^4.

%e 45 is a term because 45^2 = 9^3 + 6^4 = 729 + 1296 = 2025.

%Y Cf. A087210, solutions with gcd (n, x, y)=1.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Aug 26 2003

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