Idoneal Number

A Positive value of for which the fact that a number is a Monomorph (i.e., the number is expressible in onlyone way as or where is Relatively Prime to ) guarantees it to be a Prime,Power of a Prime, or twice one of these. The numbers are also called Euler's Idoneal Numbers, or Suitable Numbers.

The 65 idoneal numbers found by Gauß andEuler and conjectured to be the only such numbers (Shanks 1969) are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13,15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93, 102, 105, 112, 120, 130,133, 165, 168, 177, 190, 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, and1848 (Sloane's A000926).

References

Shanks, D. ``On Gauss's Class Number Problems.'' Math. Comput. 23, 151-163, 1969.

Sloane, N. J. A. SequenceA000926/M0476in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

• Pappus-Guldinus Theorem
• Pappus's Centroid Theorem
• Pappus's Harmonic Theorem
• Pappus's Hexagon Theorem
• Pappus's Theorem
• Parabiaugmented Dodecahedron
• Parabiaugmented Hexagonal Prism
• Parabiaugmented Truncated Dodecahedron
• Parabidiminished Rhombicosidodecahedron
• Parabigyrate Rhombicosidodecahedron
• Parabola
• Parabola Caustic
• Parabola Evolute
• Parabola Inverse Curve
• Parabola Involute
• Parabola Pedal Curve
• Parabolic Coordinates
• Parabolic Cyclide
• Parabolic Cylinder
• Parabolic Cylinder Function
• Parabolic Cylindrical Coordinates
• Parabolic Fixed Point
• Parabolic Geometry
• Parabolic Horn Cyclide
• Parabolic Partial Differential Equation