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Search: id:A054532
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| A054532 |
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Triangular array giving Ramanujan sum T(n,k) = c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2 Pi i m n / k), n >= 1, 1<=k<=n. |
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+0
5
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| 1, 1, 1, 1, -1, 2, 1, 1, -1, 2, 1, -1, -1, 0, 4, 1, 1, 2, -2, -1, 2, 1, -1, -1, 0, -1, 1, 6, 1, 1, -1, 2, -1, -1, -1, 4, 1, -1, 2, 0, -1, -2, -1, 0, 6, 1, 1, -1, -2, 4, -1, -1, 0, 0, 4, 1, -1, -1, 0, -1, 1, -1, 0, 0, 1, 10, 1, 1, 2, 2, -1, 2, -1, -4, -3, -1, -1, 4, 1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, 12, 1
(list; table; graph; listen)
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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
P. Moree and H. Hommerson, Value distribution of Ramanujan sums and of cyclotomic polynomial coefficients
H. G. Gadiyar and R. Padma, Linking the circle and the sieve: Ramanujan-Fourier series
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EXAMPLE
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1; 1,1; 1,-1,2; 1,1,-1,2; 1,-1,-1,0,4; 1,1,2,-2,-1,2; ...
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CROSSREFS
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Cf. A054533, A054534, A054535.
Sequence in context: A116861 A105242 A114116 this_sequence A120888 A031230 A111616
Adjacent sequences: A054529 A054530 A054531 this_sequence A054533 A054534 A054535
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KEYWORD
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sign,easy,nice,tabl
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AUTHOR
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njas, Apr 09 2000
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