%I #23 Mar 17 2021 09:31:52

%S 23,87,119,201,312,376,455,616,760,840,1055,1136,1248,1472,1719,1959,

%T 2064,2472,2764,2976,3264,3407,3584,4032,4336,4848,4992,5088,5523,

%U 5900,6112,6624,7360,7680,7680,8448,8960,9152,9856,10208,11136,11904,12256,12256

%N The largest integer that cannot be written as the sum of squares of integers larger than n.

%C Numbers can be used more than once.

%H Giovanni Resta, <a href="/A193018/b193018.txt">Table of n, a(n) for n = 2..100</a>

%H Ken Dutch and Christy Rickett, <a href="http://nntdm.net/papers/nntdm-18/NNTDM-18-1-16-21.pdf">Conductors for sets of large integer squares</a>, Notes on Number Theory and Discrete Mathematics Vol. 18 (2012), No. 1, 16-21.

%H Alessio Moscariello, <a href="https://arxiv.org/pdf/1408.1435.pdf">On integers which are representable as sums of large squares</a>, International Journal of Number Theory 11 (8) (2015), 2505-2511.

%F a(n) < n^4 + 6n^3 + 11n^2 + 6n by Sylvester's theorem. [_Charles R Greathouse IV_, Jul 14 2011]

%F a(n) = o(n^{2+e}) for all e > 0, according to Dutch and Rickett. [_Jeffrey Shallit_, Mar 17 2021]

%F a(n) = O(n^2), according to Moscariello. [_Jeffrey Shallit_, Mar 17 2021]

%t a[n_] := Block[{k = 4, f}, While[ (n+k)^2 <= (f = FrobeniusNumber[ Range[ n, n+k]^2]), k++]; f]; a /@ Range[2, 45] (* _Giovanni Resta_, Jun 13 2016 *)

%Y Cf. A191090, A191091.

%K nonn,easy

%O 2,1

%A _Remmert Borst_, Jul 14 2011