A081647 Integers congruent to 0, 1, 4, 9, 16, 25, 36 or 49 (mod 64) which are not squares.

65, 68, 73, 80, 89, 113, 128, 129, 132, 137, 153, 164, 177, 192, 193, 201, 208, 217, 228, 241, 257, 260, 265, 272, 281, 292, 305, 320, 321, 329, 336, 345, 356, 369, 384, 385, 388, 393, 409, 420, 433, 448, 449, 452, 457, 464, 473, 497, 512, 513, 516, 521, 528

Offset: 1

Author

Robert G. Wilson v, Mar 26 2003

Keywords

• easy
• nonn

References

• Mark A. Herkommer, Number Theory, A Programmer's Guide, McGraw-Hill, New York, 1999, page 315.

Programs

Mathematica

Select[ Range[546], (Mod[ #, 64] == 0 || Mod[ #, 64] == 1 || Mod[ #, 64] == 4 || Mod[ #, 64] == 9 || Mod[ #, 64] == 16 || Mod[ #, 64] == 25 || Mod[ #, 64] == 36 || Mod[ #, 64] == 49) && !IntegerQ[ Sqrt[ # ]] & ]
With[{nn=550},Select[Complement[Range[nn],Range[Ceiling[ Sqrt[nn]]]^2], MemberQ[ {0,1,4,9,16,25,36,49},Mod[#,64]]&]] (* Harvey P. Dale, Jul 26 2011 *)