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

2579, 3633, 3735, 3868, 3948, 4237, 4469, 4544, 4588, 4663, 4678, 4789, 4840, 4913, 4928, 4959, 4995, 5024, 5094, 5104, 5180, 5344, 5393, 5584, 5625, 5642, 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

Offset

1,1

Comments

Also, 6-representable numbers (Alekseyev 2019).

All integers > 15707 = A297896(6) belong to this sequence.

Links

Max Alekseyev, Table of n, a(n) for n = 1..10000

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 6-representable numbers in the interval [1,76744] and their 6-representations (see Alekseyev 2019 paper for details)

Formula

For n >= 5484, a(n) = n + 10224.

Example

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.

Crossrefs

Cf. A051882, A051909, A052428, A297895, A297896.

Sequence in context: A217183 A034415 A201510 * A235094 A171257 A252159

Adjacent sequences: A303397 A303398 A303399 * A303401 A303402 A303403

Keyword

nonn,easy

Author

Max Alekseyev, Apr 23 2018

Status

approved