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

1,5

Comments

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, Oct 31 2007

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

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

Mathematica

a[n_] := Count[PrimitiveRootList[(p = Prime[n+1])], _?(CoprimeQ[#, (p-1)] &)]; Array[a, 70] (* James C. McMahon, Jan 12 2025 *)

Crossrefs

Sequence in context: A066248 A065164 A138124 * A019680 A249144 A080032

Adjacent sequences: A128857 A128858 A128859 * A128861 A128862 A128863

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 20 2007

Extensions

More terms from R. J. Mathar, Oct 31 2007

Status

approved