A094447 - OEIS

%I #11 Jun 13 2020 02:39:48

%S 65,91,351,468,520,559,637,728,793,1001,1027,1339,1456,1547,1729,1755,

%T 2457,2808,3718,3744,3887,4160,4394,4472,4706,4914,4940,5096,5642,

%U 5824,6175,6344,7163,7202,7371,7657,8008,8125,8190,8216,9009

%N Numbers which are the sum of two positive cubes and divisible by 13.

%H Vincenzo Librandi, <a href="/A094447/b094447.txt">Table of n, a(n) for n = 1..1000</a>

%e Sums not divisible by 13 are shown in asterisks:

%e ....|...1....8...27...64...125...216...343...512...729..1000..1331

%e ------------------------------------------------------------------

%e 1...|...*....*....*...65.....*.....*.....*.....*.....*..1001.....*

%e 8...|...*....*....*....*.....*.....*...351...520.....*.....*..1339

%e 27..|...*....*....*...91.....*.....*.....*.....*.....*..1027.....*

%e 64..|..65....*...91....*.....*.....*.....*.....*...793.....*.....*

%e 125.|...*....*....*....*.....*.....*...468...637.....*.....*..1456

%e 216.|...*....*....*....*.....*.....*...559...728.....*.....*..1547

%e 343.|...*..351....*....*...468...559.....*.....*.....*.....*.....*

%e 512.|...*..520....*....*...637...728.....*.....*.....*.....*.....*

%e 729.|...*....*....*..793.....*.....*.....*.....*.....*..1729.....*

%e 1000|1001....*.1027....*.....*.....*.....*.....*..1729.....*.....*

%e 1331|...*.1339....*....*..1456..1547.....*.....*.....*.....*.....*

%t upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 13] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[10^4] (* _Giovanni Resta_, Jun 12 2020 *)

%K nonn,easy

%O 1,1

%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jun 09 2004

%E Definition corrected by _Robert Israel_, Jun 12 2020