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%I #29 Sep 08 2022 08:46:04
%S 6119,6293,6641,7163,7859,8729,9773,10991,12383,13949,15689,17603,
%T 19691,21953,48778,48952,49474,50344,51562,53128,55042,57304,59914,
%U 62872,66178,69832,73834,78184,82882,87928,93322,99064,105154
%N Numbers which are the sum of two positive cubes and divisible by 29.
%C If 12*h-2523 is a square then some values of 29*h are in this sequence.
%C It is easy to verify that h is of the form 3*m^2-9*m+217, and therefore 29*(3*m^2-9*m+217) = (16-m)^3+(m+13)^3. [_Bruno Berselli_, May 10 2013]
%H Vincenzo Librandi, <a href="/A224483/b224483.txt">Table of n, a(n) for n = 1..1000</a>
%t upto[n_] := Block[{t}, Union@Reap[ Do[If[Mod[t = x^3 + y^3, 29] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[106000] (* _Giovanni Resta_, Jun 12 2020 *)
%o (Magma) [n: n in [2..2*10^5] | exists{i: i in [1..Iroot(n-1,3)] | IsPower(n-i^3,3) and IsZero(n mod 29)}]; // _Bruno Berselli_, May 10 2013
%Y Cf. numbers which are the sum of two positive cubes and divisible by k: A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A102658 (k=31), A102618 (k=37).
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, May 08 2013
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