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A291828 Numbers k such that k^2 is sum of two positive 7th powers. 1
16, 2048, 34992, 262144, 1250000, 4478976, 13176688, 33554432, 76527504, 160000000, 276922881, 311794736, 573308928, 1003976272, 1686616064, 2733750000, 4294967296, 6565418768, 9795520512, 14301947824, 20480000000, 28817416656, 35446128768, 39909726208 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

When a^7 + b^7 = m, (ma)^7 + (mb)^7 = m^8 is square.

When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..447

EXAMPLE

16^2 = 2^8 = 2^7 + 2^7, so 16 is in the sequence.

276922881^2 = 129^7 + 358^7, so 276922881 is in the sequence.

MATHEMATICA

lst={}; Do[If[IntegerQ[(n^2-a^7)^(1/7)], AppendTo[lst, n]], {n, 4*10^10}, {a, (n^2/2)^(1/7)}]; lst

CROSSREFS

Cf. A000290, A001015, A004431, A050801.

Sequence in context: A265213 A176886 A159389 * A086804 A317450 A121366

Adjacent sequences:  A291825 A291826 A291827 * A291829 A291830 A291831

KEYWORD

nonn

AUTHOR

XU Pingya, Sep 03 2017

STATUS

approved

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)