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%I #25 Jan 16 2024 05:02:17
%S 1,4,8,9,25,27,36,49,72,100,108,121,125,169,196,200,216,225,243,289,
%T 343,361,392,441,484,500,529,675,676,841,900,961,968,972,1000,1089,
%U 1125,1156,1225,1323,1331,1352,1369,1372,1444,1521,1681,1764,1800,1849,1944,2116,2197,2209,2312,2401,2601,2700,2744,2809,2888
%N Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^s/m) <> 0 for all s>=2.
%C Conjecture 1: This is a subset of A001694.
%C Conjecture 2: This sequence contains all the terms from A338325, plus 243, 972, 1944, 2401, ...
%t Select[Range[1, 200], Product[Abs[Sum[N[E^(2*Pi*I*k^s/#), 100], {k, 0, #-1}]], {s, 2, 200}] > 0 &]
%Y Cf. A001074, A042965, A368812.
%Y Cf. A001694, A338325.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Jan 10 2024
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