|
%I #30 Sep 08 2019 14:28:19
%S 1,49,200,338,418,445,486,489,530,569,609,610,653,770,775,804,845,855,
%T 898,899,939,978,1005,1019,1049,1065,1085,1090,1134,1194,1207,1213,
%U 1214,1254,1281,1308,1356,1374,1379,1382,1415,1434,1442,1457,1458,1459,1475,1499,1502,1522,1543,1566,1570,1582
%N Numbers that can be partitioned into squares of distinct integers whose reciprocals sum to 1.
%C All integers > 8542 = A297896(1) belong to this sequence.
%H Max Alekseyev, <a href="/A297895/b297895.txt">Table of n, a(n) for n = 1..5000</a>
%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.
%H Max Alekseyev, <a href="/A297895/a297895.txt">List of all representable numbers in the interval [1,54533] and their representations</a> (see Alekseyev 2019 paper for details)
%F For n >= 4496, a(n) = n + 4047.
%e 49 = 2^2 + 3^2 + 6^2, where 1/2 + 1/3 + 1/6 = 1;
%e 200 = 2^2 + 4^2 + 6^2 + 12^2, where 1/2 + 1/4 + 1/6 + 1/12 = 1;
%e 338 = 2^2 + 3^2 + 10^2 + 15^2, where 1/2 + 1/3 + 1/10 + 1/15 = 1.
%Y Cf. A051882, A051909, A052428, A297896, A303400.
%K nonn
%O 1,2
%A _Max Alekseyev_, Jan 08 2018
|
