A368959 Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^s/m) <> 0 for all s>=2.

1, 4, 8, 9, 25, 27, 36, 49, 72, 100, 108, 121, 125, 169, 196, 200, 216, 225, 243, 289, 343, 361, 392, 441, 484, 500, 529, 675, 676, 841, 900, 961, 968, 972, 1000, 1089, 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

Offset

1,2

Comments

Conjecture 1: This is a subset of A001694.

Conjecture 2: This sequence contains all the terms from A338325, plus 243, 972, 1944, 2401, ...

Links

Table of n, a(n) for n=1..61.

Mathematica

Select[Range[1, 200], Product[Abs[Sum[N[E^(2*Pi*I*k^s/#), 100], {k, 0, #-1}]], {s, 2, 200}] > 0 &]

Crossrefs

Cf. A001074, A042965, A368812.

Cf. A001694, A338325.

Sequence in context: A076702 A051761 A153326 * A338325 A168363 A182046

Adjacent sequences: A368956 A368957 A368958 * A368960 A368961 A368962

Keyword

nonn

Author

Vaclav Kotesovec, Jan 10 2024

Status

approved