A291850 - OEIS

A291850

Numbers k such that k^2 is the sum of two positive 5th powers.

8, 256, 1944, 6655, 8192, 25000, 35937, 62208, 134456, 212960, 262144, 344605, 453962, 472392, 692759, 800000, 1149984, 1288408, 1617165, 1990656, 2970344, 4302592, 6075000, 6814720, 8388608, 8732691, 11358856, 14526784, 15116544, 19808792, 20796875, 22168288

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OFFSET

1,1

COMMENTS

If a^5 + b^5 = m, then (ma)^5 + (mb)^5 = m^6 = (m^3)^2 is square. Therefore A003347(n)^3 are terms of this sequence.

When k in this sequence, k * (n^5) (n = 2, 3, ... ) is also in this sequence.

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

8^2 = 2^5 + 2^5, so 8 is in the sequence.

6655^2 = 22^5 + 33^5, so 6655 is in the sequence.

MATHEMATICA