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A291850 Numbers k such that k^2 is the sum of two positive 5th powers. 0
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 (list; graph; refs; listen; history; text; internal format)
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 is 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

lst={}; Do[If[IntegerQ[(n^2-a^5)^(1/5)], AppendTo[lst, n^2]], {n, 7000}, {a, n^2/2)^(1/5)}]; lst

CROSSREFS

Cf. A000404, A004431, A003325, A050801, A003336, A003347.

Sequence in context: A034674 A317511 A300176 * A130034 A128787 A013824

Adjacent sequences:  A291847 A291848 A291849 * A291851 A291852 A291853

KEYWORD

nonn

AUTHOR

XU Pingya, Sep 04 2017

STATUS

approved

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Last modified June 13 11:36 EDT 2021. Contains 344990 sequences. (Running on oeis4.)