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A054533
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Triangular array giving Ramanujan sum T(n,k) = c_n(k), for n >= 1, 1<=k<=n, where c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2 Pi i m n / k).
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13
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1, -1, 1, -1, -1, 2, 0, -2, 0, 2, -1, -1, -1, -1, 4, 1, -1, -2, -1, 1, 2, -1, -1, -1, -1, -1, -1, 6, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -3, 0, 0, -3, 0, 0, 6, 1, -1, 1, -1, -4, -1, 1, -1, 1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 0, 2, 0, -2, 0, -4, 0, -2, 0, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 12, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 160.
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LINKS
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T. D. Noe, Rows n=1..50 of triangle, flattened
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EXAMPLE
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1; -1,1; -1,-1,2; 0,-2,0,2; -1,-1,-1,-1,4; ...
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MATHEMATICA
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c[k_, n_] := Sum[ If[GCD[m, k] == 1, Exp[2 Pi*I*m*n/k], 0], {m, 1, k}]; A054533 = Flatten[ Table[c[n, k] // FullSimplify, {n, 1, 14}, {k, 1, n}] ] (* Jean-François Alcover, Jun 27 2012 *)
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CROSSREFS
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Cf. A054532, A054534, A054535.
Sequence in context: A026613 A117199 A052511 * A143232 A096030 A025815
Adjacent sequences: A054530 A054531 A054532 * A054534 A054535 A054536
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KEYWORD
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sign,easy,nice,tabl
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AUTHOR
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N. J. A. Sloane, Apr 09 2000
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STATUS
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approved
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