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

Author

Max Alekseyev, Apr 23 2018

Keywords

• nonn
• easy

Comments

Also, 6-representable numbers (Alekseyev 2019).

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

Examples

			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.
		

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)

Crossrefs

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

Formula

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