

A291851


Numbers k such that k^3 is the sum of two positive 5th powers.


0



4, 128, 972, 1089, 4096, 12500, 31104, 34848, 59536, 67228, 75625, 131072, 236196, 264627, 400000, 644204, 995328, 1050625, 1115136, 1485172, 1605289, 1905152, 2151296, 2420000, 3037500, 3403125, 4194304, 5679428, 7558272, 8468064, 9771876, 9904396, 9966649
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OFFSET

1,1


COMMENTS

If a^5 + b^5 = m, then (ma)^5 + (mb)^5 = m^6 = (m^2)^3 is a cube. Therefore the square of each term of A003347 is a term of this sequence.
When k is in this sequence, k * (n^5), for n > 1, is also in this sequence.


LINKS

Table of n, a(n) for n=1..33.


EXAMPLE

4^3 = 2^6 = 2^5 + 2^5, so 4 is in the sequence.
1089^3 = 33^5 + 66^5, so 1089 is in the sequence.


MATHEMATICA

lst={}; Do[If[IntegerQ[(n^3a^5)^(1/5)], AppendTo[lst, n]], {n, 10^7}, {a, (n^3/2)^(1/5)}]; lst


CROSSREFS

Cf. A000404, A004431, A003325, A050801, A003336, A003347.
Sequence in context: A070781 A152421 A270959 * A128790 A267796 A013823
Adjacent sequences: A291848 A291849 A291850 * A291852 A291853 A291854


KEYWORD

nonn


AUTHOR

XU Pingya, Sep 04 2017


STATUS

approved



