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Search: id:A128860
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| A128860 |
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Let p = n-th odd prime; a(n) = number of primitive roots of p which are relatively prime to p-1. |
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+0
1
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| 0, 1, 1, 1, 2, 4, 1, 6, 5, 3, 5, 6, 3, 13, 11, 10, 5, 5, 10, 8, 9, 16, 19, 11, 16, 10, 22, 13, 23, 12, 15, 30, 9, 35, 8, 17, 15, 46, 41, 37, 14, 34, 20, 36, 16, 10, 21, 49, 26, 54, 43, 17, 38, 64, 71, 65, 23, 32, 33, 22, 71, 30, 56, 28, 77, 16, 26, 79, 38, 74
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The number of primitive roots without the restriction of relative-primality is in A008330, so a(n)<=A008330(n+1). A table of prime moduli is in A128250. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2007
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REFERENCES
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R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, Austin, TX, 1961, pp. 69-70.
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MAPLE
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A128250 := proc(g, p) local k ; if gcd(g, p) > 1 then RETURN(0) ; fi ; for k from 1 do if (g^k mod p ) = 1 then RETURN(k) ; fi ; od: end: proots := proc(p) local a, g ; a := 0 ; for g from 1 to p do if A128250(g, p) = p-1 and gcd(g, p-1) = 1 then a := a+1 ; fi ; od: RETURN(a) ; end: A128860 := proc(n) local p; p := ithprime(n+1) ; proots(p) ; end: seq(A128860(n), n=1..60) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2007
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CROSSREFS
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Sequence in context: A066248 A065164 A138124 this_sequence A019680 A080032 A105357
Adjacent sequences: A128857 A128858 A128859 this_sequence A128861 A128862 A128863
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Apr 20 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2007
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