A297895 Numbers that can be partitioned into squares of distinct integers whose reciprocals sum to 1.

1, 49, 200, 338, 418, 445, 486, 489, 530, 569, 609, 610, 653, 770, 775, 804, 845, 855, 898, 899, 939, 978, 1005, 1019, 1049, 1065, 1085, 1090, 1134, 1194, 1207, 1213, 1214, 1254, 1281, 1308, 1356, 1374, 1379, 1382, 1415, 1434, 1442, 1457, 1458, 1459, 1475, 1499, 1502, 1522, 1543, 1566, 1570, 1582

Offset

1,2

Comments

All integers > 8542 = A297896(1) belong to this sequence.

Links

Max Alekseyev, Table of n, a(n) for n = 1..5000

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:10.2307/j.ctvd58spj.18 Preprint arXiv:1801.05928 [math.NT], 2018.

Max Alekseyev, List of all representable numbers in the interval [1,54533] and their representations (see Alekseyev 2019 paper for details)

Formula

For n >= 4496, a(n) = n + 4047.

Example

49 = 2^2 + 3^2 + 6^2, where 1/2 + 1/3 + 1/6 = 1;
200 = 2^2 + 4^2 + 6^2 + 12^2, where 1/2 + 1/4 + 1/6 + 1/12 = 1;
338 = 2^2 + 3^2 + 10^2 + 15^2, where 1/2 + 1/3 + 1/10 + 1/15 = 1.

Crossrefs

Cf. A051882, A051909, A052428, A297896, A303400.

Sequence in context: A351663 A016982 A157919 * A204709 A192359 A100453

Adjacent sequences: A297892 A297893 A297894 * A297896 A297897 A297898

Keyword

nonn

Author

Max Alekseyev, Jan 08 2018

Status

approved