A128860 Let p be the n-th odd prime; a(n) is the number of primitive roots of p which are relatively prime to p-1.
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
Offset: 1
References
- R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, Austin, TX, 1961, pp. 69-70.
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
Programs
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Maple
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, Oct 31 2007
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Mathematica
a[n_] := Count[PrimitiveRootList[(p = Prime[n+1])], ?(CoprimeQ[#, (p-1)] &)]; Array[a, 70] (* _James C. McMahon, Jan 12 2025 *)
Extensions
More terms from R. J. Mathar, Oct 31 2007
Comments