A297896 - OEIS

A297896

Largest integer that cannot be represented as x1^2 + ... + xk^2, where k >= 1, n <= x1 < ... < xk, and 1/x1 + ... + 1/xk = 1.

%I #17 Sep 08 2019 14:27:25

%S 8542,8542,8623,9623,12367,15707,19116,24317

%N Largest integer that cannot be represented as x1^2 + ... + xk^2, where k >= 1, n <= x1 < ... < xk, and 1/x1 + ... + 1/xk = 1.

%C Terms a(1)=a(2)=8542 correspond to sequence A297895, and a(6)=15707 corresponds to sequence A303400.

%H 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.

%Y Cf. A297895, A303400.

%K nonn,more

%O 1,1

%A _Max Alekseyev_, Jan 20 2018