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A297895 Numbers that can be partitioned into squares of distinct integers whose reciprocals sum to 1. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
All integers > 8542 = A297896(1) belong to this sequence.
LINKS
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.
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
Sequence in context: A351663 A016982 A157919 * A204709 A192359 A100453
KEYWORD
nonn
AUTHOR
Max Alekseyev, Jan 08 2018
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)