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 A123475 Product of the primitive roots of prime(n). 6
 1, 2, 6, 15, 672, 924, 11642400, 163800, 109681110000, 5590307923200, 970377408, 134088514560000, 138960660963091968000, 874927557504000, 3456156426256013065185600000000, 30688148115024695887527936000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Except for n=2, we have a(n)=1 (mod prime(n)). REFERENCES C. F. Gauss, Disquisitiones Arithmeticae, Yale, 1965; see p. 52. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..145 EXAMPLE a(5)=672 because the primitive roots of 11 are {2,6,7,8}. MATHEMATICA PrimRoots[p_] := Select[Range[p-1], MultiplicativeOrder[ #, p]==p-1&]; Table[Times@@PrimRoots[Prime[n]], {n, 20}] Times@@@Table[PrimitiveRootList[Prime[n]], {n, 20}] (* Harlan J. Brothers, Sep 02 2023 *) PROG (PARI) vecprod(v)=prod(i=1, #v, v[i]) a(n, p=prime(n))=vecprod(select(n->znorder(Mod(n, p))==p-1, [2..p-1])) apply(p->a(0, p), primes(20)) \\ Charles R Greathouse IV, May 15 2015 (Perl) use ntheory ":all"; sub list { my \$n=shift; grep { znorder(\$_, \$n) == \$n-1 } 2..\$n-1; } say vecprod(list(\$_)) for @{primes(nth_prime(20))}; # Dana Jacobsen, May 15 2015 CROSSREFS Cf. A060749 (primitive roots of prime(n)), A088144 (sum of primitive roots of prime(n)). Sequence in context: A261726 A302775 A181993 * A193341 A009711 A009586 Adjacent sequences: A123472 A123473 A123474 * A123476 A123477 A123478 KEYWORD nonn AUTHOR T. D. Noe, Sep 27 2006 STATUS approved

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Last modified December 5 03:04 EST 2023. Contains 367567 sequences. (Running on oeis4.)