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%I #13 Jul 29 2021 09:30:51
%S 1,4,7,8,9,13,19,25,27,28,31,32,36,37,43,49,52,56,61,63,64,67,72,73,
%T 76,79,91,97,100,103,104,108,109,117,121,124,125,127,133,139,148,151,
%U 152,157,163,169,171,172,175,181,189,193,196,199,200,211,216,217
%N Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^3/m) != 0.
%C 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.
%H T. D. Noe, <a href="/A001074/b001074.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%e 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.
%t Select[Range[300], Sum[Exp[2 Pi*I*k^3/#], {k, 0, # - 1}] != 0 &] (* _T. D. Noe_, Jun 25 2012 *)
%K nice,nonn,easy
%O 1,2
%A R. Lozyniak (11(AT)onna.com)
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