

A001074


Numbers n such that Sum_{k=0..n1} exp(2*Pi*i*k^3/n) != 0.


1



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
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OFFSET

1,2


COMMENTS

Mark n points around horizontal disk with labels 0..n1; place coins at positions k^3 mod n for k=0..n1; sequence gives n's for which disk does not balance.


LINKS

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


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Sequence in context: A289631 A076680 A235623 * A214206 A026316 A283767
Adjacent sequences: A001071 A001072 A001073 * A001075 A001076 A001077


KEYWORD

nice,nonn,easy


AUTHOR

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


STATUS

approved



