A001074 Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^3/m) != 0.

1, 4, 7, 8, 9, 13, 19, 25, 27, 28, 31, 32, 36, 37, 43, 49, 52, 56, 61, 63, 64, 67, 72, 73, 76, 79, 91, 97, 100, 103, 104, 108, 109, 117, 121, 124, 125, 127, 133, 139, 148, 151, 152, 157, 163, 169, 171, 172, 175, 181, 189, 193, 196, 199, 200, 211, 216, 217

Offset: 1

Author

R. Lozyniak (11(AT)onna.com)

Keywords

• nice
• nonn
• easy

Comments

Mark m points around a horizontal disk with labels 0..m-1; place coins at positions k^3 mod m for k=0..m-1; sequence gives values of m for which the disk is not balanced.

Examples

			8 is in the sequence because 4 coins go at 0, and 1 each at 1, 3, 5, 7, so the disk is unbalanced in the direction of point 0.
12 is not in the sequence because there are 2 coins at 0, 4, 8 and 1 coin at 1, 3, 5, 7, 9, 11, so the disk is balanced.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Select[Range[300], Sum[Exp[2 Pi*I*k^3/#], {k, 0, # - 1}] != 0 &] (* T. D. Noe, Jun 25 2012 *)