Geodesic
On the largest integer that is not a sum of distinct positive \(n\)th powers
Journal of integer sequences, Tome 20 (2017) no. 7
It is known that for an arbitrary positive integer $n$ the sequence $S(x^{n}) = (1^{n}, 2^{n}, \dots )$ is complete, meaning that every sufficiently large integer is a sum of distinct $n$th powers of positive integers. We prove that every integer $m \ge (b - 1)2^{n-1}$(r + (2/3)$(b - 1)(2^{2n} - 1) + 2(b - 2))^{n} - 2a + ab$, where $a = n!2^{n^{2}}, b= 2^{n^{3}}a^{n-1}, r = 2^$n^2$ - n}a$, is a sum of distinct positive $n$th powers.
Classification : 11P05, 05A17
Keywords: complete sequence, threshold of completeness, sum of powers 
@article{JIS_2017__20_7_a7,
     author = {Kim,  Doyon},
     title = {On the largest integer that is not a sum of distinct positive \(n\)th powers},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {7},
     zbl = {1427.11098},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a7/}
}
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Kim,  Doyon. On the largest integer that is not a sum of distinct positive \(n\)th powers. Journal of integer sequences, Tome 20 (2017) no. 7. http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a7/