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A060839
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Number of non-congruent solutions of x^3 == 1 mod n.
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6
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1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 3, 3, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 3, 1, 1, 1, 3, 3, 9, 1, 3, 1, 3, 1, 1, 3, 1, 3, 3, 3, 1, 3, 3, 3, 3, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 3, 9, 1, 3, 1, 3, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Sum(k=1,n,a(k)) appears to be asymptotic to C*n*Log(n) with C=0.4... - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 19 2002
Multiplicative with a(3) = 1, a(3^e) = 3, e >= 2, a((3k+1)^e) = 3, a((3k+2)^e) = 1. David W. Wilson (davidwwilson(AT)comcast.net) May 22, 2005.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n (arXiv:math.NT/0604465).
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FORMULA
| Let b(n) be the number of primes dividing n which are congruent to 1 mod 3 (sequence A005088); then a(n) is 3^b(n) if n is not divisible by 9 and 3^(b(n) + 1) if n is divisible by 9.
Sequence is multiplicative. - David W. Wilson, Jan 06 2005.
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EXAMPLE
| a(7) = 3 because the three solutions to x^3 == 1 mod 7 are: x = 1,2,4
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MATHEMATICA
| a[n_] := Sum[ If[ Mod[k^3-1, n] == 0, 1, 0], {k, 1, n}]; Table[ a[n], {n, 1, 105}](* From Jean-François Alcover, Nov 14 2011, after Pari *)
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PROG
| (PARI) a(n)=sum(i=1, n, if((i^3-1)%n, 0, 1))
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CROSSREFS
| A005088, A060594.
Sequence in context: A051718 A016472 A095346 * A088204 A100375 A066975
Adjacent sequences: A060836 A060837 A060838 * A060840 A060841 A060842
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KEYWORD
| nonn,nice,easy,mult
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), May 02 2001
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001
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