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Search: id:A054535
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| A054535 |
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Square array giving Ramanujan sum T(n,k) = c_n(k), where c_k(n) = Sum_{m=1..k, (m,k)=1} exp(2 Pi i m n / k), read by antidiagonals (n >= 1, k >= 1). |
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+0
5
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| 1, -1, 1, -1, 1, 1, 0, -1, -1, 1, -1, -2, 2, 1, 1, 1, -1, 0, -1, -1, 1, -1, -1, -1, 2, -1, 1, 1, 0, -1, -2, -1, 0, 2, -1, 1, 0, 0, -1, -1, 4, -2, -1, 1, 1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1, -1, -1, -3, -4, -1, 2, -1, 2, 2, 1, 1, 0, -1, 1, 0, 0, -1, 1, -1, 0, -1, -1, 1, -1, 2, -1, -1, 0, 0, 6, -1, -1, -2, -1, 1, 1, 1, -1
(list; table; graph; listen)
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OFFSET
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1,12
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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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FORMULA
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T(n, k)=phi(n)*mobius(n/gcd(n, k))/phi(n/gcd(n, k)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 23 2004
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EXAMPLE
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Square array starts:
1, -1, -1, 0, -1, ...
1, 1, -1, -2, -1, ...
1, -1, 2, 0, -1, ...
1, 1, -1, 2, -1, ...
1, -1, -1, 0, 4, ...
...
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MAPLE
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with(numtheory): c:=(n, k)->phi(n)*mobius(n/gcd(n, k))/phi(n/gcd(n, k)): for n from 1 to 13 do seq(c(n+1-j, j), j=1..n) od; # gives the sequence in triangular form (Deutsch)
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CROSSREFS
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Transpose of array in A054534. Cf. A054532, A054533.
Sequence in context: A111915 A066520 A088526 this_sequence A054534 A085769 A102552
Adjacent sequences: A054532 A054533 A054534 this_sequence A054536 A054537 A054538
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KEYWORD
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sign,tabl,nice
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AUTHOR
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njas, Apr 09 2000
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