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A123475
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Product of the primitive roots of prime(n).
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6
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1, 2, 6, 15, 672, 924, 11642400, 163800, 109681110000, 5590307923200, 970377408, 134088514560000, 138960660963091968000, 874927557504000, 3456156426256013065185600000000, 30688148115024695887527936000000
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OFFSET
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1,2
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COMMENTS
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Except for n=2, we have a(n)=1 (mod prime(n)).
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REFERENCES
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C. F. Gauss, Disquisitiones Arithmeticae, Yale, 1965; see p. 52.
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LINKS
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EXAMPLE
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a(5)=672 because the primitive roots of 11 are {2,6,7,8}.
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MATHEMATICA
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PrimRoots[p_] := Select[Range[p-1], MultiplicativeOrder[ #, p]==p-1&]; Table[Times@@PrimRoots[Prime[n]], {n, 20}]
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PROG
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(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]))
(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
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CROSSREFS
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Cf. A060749 (primitive roots of prime(n)), A088144 (sum of primitive roots of prime(n)).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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