

A108380


Least number of distinct nth roots of unity summing to the smallest possible nonzero magnitude.


4



1, 1, 1, 1, 2, 1, 2, 3, 2, 3, 5, 5, 6, 6, 4, 5, 5, 5, 7, 7, 10, 5, 8, 7, 12, 7, 10, 9, 14, 13, 11, 7, 14, 11, 17, 9, 18, 14, 18, 9, 19, 12, 17, 15, 14, 14, 22, 15, 16, 20, 20, 17, 18, 22, 23, 17, 24, 19, 26, 21, 29, 18, 26, 19, 26, 31, 30, 27, 31, 17, 32, 23, 34
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OFFSET

1,5


COMMENTS

Myerson writes about the unsolved problem of finding a good lower bound on the least magnitude as a function of n. Note that a(n)<n/2 for n>2 because the sum of all nth roots of unity is 0.


LINKS



EXAMPLE

a(8)=3 because the least nonzero magnitude is sqrt(2)1, which is the sum of three 8th roots of unity.


CROSSREFS

Cf. A103314 (number of subsets of the nth roots of unity summing to zero).


KEYWORD

nonn


AUTHOR



STATUS

approved



