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A303400 Numbers that can be partitioned into squares of distinct integers >= 6, whose reciprocals sum to 1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, 6-representable numbers (Alekseyev 2018).

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

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Last modified August 6 11:55 EDT 2020. Contains 336246 sequences. (Running on oeis4.)