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Search: id:A114643
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| A114643 |
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Number of real primitive Dirichlet characters modulo n. |
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+0
4
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| 1, 0, 1, 1, 1, 0, 1, 2, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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a(n)=1 if n=1; a(n)=1 if either n or -n is a fundamental discriminant (not both); a(n)=2 if n and -n are fundamental discriminants; a(n)=0 otherwise. Also, sum(k=1,n,a(k)) is asymptotic to (6/pi^2)*n.
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REFERENCES
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W. Ellison and F. Ellison, Prime Numbers, Wiley, 1985, pp. 224-226.
I. J. Zucker and M. M. Robertson, Some properties of Dirichlet L-series, J. Phys. A 9 (1976) 1207-1214.
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LINKS
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Eric Weisstein's World of Mathematics, Dirichlet L-Series.
S. R. Finch, Cubic and quartic characters. [From S. R. Finch (Steven.Finch(AT)inria.fr), Jun 09 2009]
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FORMULA
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This sequence is multiplicative with a(2)=0, a(4)=1, a(8)=2, a(2^r)=0 for r>2, a(p)=1 for prime p>2 and a(p^r)=0 for r>1. - S. R. Finch (Steven.Finch(AT)inria.fr), Mar 08 2006
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PROGRAM
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(PARI) a(n)=sum(d=1, n, if(n%d==0, moebius(n/d)*sum(i=1, d, if((i^2-1)%d, 0, 1)), 0)) [From S. R. Finch (Steven.Finch(AT)inria.fr), Jun 09 2009]
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CROSSREFS
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Cf. A003657, A003658.
Sequence in context: A067255 A065716 A079409 this_sequence A038498 A060952 A037844
Adjacent sequences: A114640 A114641 A114642 this_sequence A114644 A114645 A114646
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KEYWORD
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nonn,mult
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AUTHOR
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S. R. Finch (Steven.Finch(AT)inria.fr), Feb 16 2006
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