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 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 (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^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 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^3-a^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

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Last modified July 30 10:27 EDT 2021. Contains 346359 sequences. (Running on oeis4.)