%I #15 Sep 08 2022 08:45:05
%S 4,9,16,25,36,49,64,81,100,121,144,169,196,225,211,289,324,361,400,
%T 441,484,529,576,625,676,729,784,841,900,961,1024,1089,1156,1225,466,
%U 1369,1444,1075,1600,1681,1764,1849,1936,2025,2116,2209,2304,2401,2500,2601
%N a(n) is the smallest k > n such that (k^3 - 1)/(n^3 - 1) is an integer.
%C For almost all n, a(n) = n^2. Exceptions: a(16) = 211, a(36) = 466, a(39) = 1075, a(53) = 1173, a(58) = 919...
%H Jinyuan Wang, <a href="/A069821/b069821.txt">Table of n, a(n) for n = 2..1000</a>
%o (PARI) a(n) = {k=n+1;while((k^3-1)%(n^3-1)>0,k++);k;} \\ _Jinyuan Wang_, Jul 29 2019
%o (Magma) sol:=[]; m:=1; for n in [2..50] do for k in [n+1..3000] do if IsIntegral((k^3-1)/(n^3-1)) then sol[m]:=k; m:=m+1; break; end if; end for; end for; sol; // _Marius A. Burtea_, Jul 30 2019
%K easy,nonn
%O 2,1
%A _Benoit Cloitre_, Apr 28 2002
%E Name clarified by _Jon E. Schoenfield_, Jul 28 2019