

A297895


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


3



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
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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, On partitions into squares of distinct integers whose reciprocals sum to 1, preprint, arXiv:1801.05928 [math.NT], 2017.
Max Alekseyev, List of all representable numbers in the interval [1,54533] and their representations (see Alekseyev 2017 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: A198386 A016982 A157919 * A204709 A192359 A100453
Adjacent sequences: A297892 A297893 A297894 * A297896 A297897 A297898


KEYWORD

nonn


AUTHOR

Max Alekseyev, Jan 08 2018


STATUS

approved



