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A303400 Numbers that can be partitioned into squares of distinct integers >= 6, whose reciprocals sum to 1.

%I A303400 #33 Jul 18 2021 10:12:48
%S A303400 2579,3633,3735,3868,3948,4237,4469,4544,4588,4663,4678,4789,4840,
%T A303400 4913,4928,4959,4995,5024,5094,5104,5180,5344,5393,5584,5625,5642,
%U A303400 5689,5704,5717,5744,5790,5799,5804,5808,5856,5865,5877,5900,5909,5921,5923,5938,5952,5953,5957,5967,5984,6013,6032,6034,6040,6049,6114,6130,6148,6150,6196,6200,6234,6246,6248,6272,6284,6287
%N A303400 Numbers that can be partitioned into squares of distinct integers >= 6, whose reciprocals sum to 1.
%C A303400 Also, 6-representable numbers (Alekseyev 2019).
%C A303400 All integers > 15707 = A297896(6) belong to this sequence.
%H A303400 Max Alekseyev, <a href="/A303400/b303400.txt">Table of n, a(n) for n = 1..10000</a>
%H A303400 Max Alekseyev (2019). On partitions into squares of distinct integers whose reciprocals sum to 1. In: J. Beineke, J. Rosenhouse (eds.) The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Volume 3, Princeton University Press, pp. 213-221. ISBN 978-0-691-18257-5 DOI:<a href="http://doi.org/10.2307/j.ctvd58spj.18">10.2307/j.ctvd58spj.18</a> Preprint <a href="https://arxiv.org/abs/1801.05928">arXiv:1801.05928 [math.NT]</a>, 2018.
%H A303400 Max Alekseyev, <a href="/A303400/a303400.txt">List of all 6-representable numbers in the interval [1,76744] and their 6-representations</a> (see Alekseyev 2019 paper for details)
%F A303400 For n >= 5484, a(n) = n + 10224.
%e A303400 2579 = 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 12^2 + 14^2 + 15^2 + 18^2 + 24^2 + 28^2, where 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/18 + 1/24 + 1/28 = 1.
%Y A303400 Cf. A051882, A051909, A052428, A297895, A297896.
%K A303400 nonn,easy
%O A303400 1,1
%A A303400 _Max Alekseyev_, Apr 23 2018