A094447 Numbers which are the sum of two positive cubes and divisible by 13.

65, 91, 351, 468, 520, 559, 637, 728, 793, 1001, 1027, 1339, 1456, 1547, 1729, 1755, 2457, 2808, 3718, 3744, 3887, 4160, 4394, 4472, 4706, 4914, 4940, 5096, 5642, 5824, 6175, 6344, 7163, 7202, 7371, 7657, 8008, 8125, 8190, 8216, 9009

Offset: 1

Author

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

Keywords

• nonn
• easy

Examples

			Sums not divisible by 13 are shown in asterisks:
....|...1....8...27...64...125...216...343...512...729..1000..1331
------------------------------------------------------------------
1...|...*....*....*...65.....*.....*.....*.....*.....*..1001.....*
8...|...*....*....*....*.....*.....*...351...520.....*.....*..1339
27..|...*....*....*...91.....*.....*.....*.....*.....*..1027.....*
64..|..65....*...91....*.....*.....*.....*.....*...793.....*.....*
125.|...*....*....*....*.....*.....*...468...637.....*.....*..1456
216.|...*....*....*....*.....*.....*...559...728.....*.....*..1547
343.|...*..351....*....*...468...559.....*.....*.....*.....*.....*
512.|...*..520....*....*...637...728.....*.....*.....*.....*.....*
729.|...*....*....*..793.....*.....*.....*.....*.....*..1729.....*
1000|1001....*.1027....*.....*.....*.....*.....*..1729.....*.....*
1331|...*.1339....*....*..1456..1547.....*.....*.....*.....*.....*
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Mathematica

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 *)

Extensions

Definition corrected by Robert Israel, Jun 12 2020