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A222009 (Product(primitive roots of p) - 1)/p, where p = prime(n) and n > 2. 3

%I

%S 1,2,61,71,684847,8621,4768743913,192769238731,31302497,3624013907027,

%T 3389284413733950439,20347152500093,73535243111830065216714893617,

%U 579021662547635771462791245283,38283945111344558723552263341142779661,60296900399609972459,271233083114844569997128597,1382959355737627871079165208413804169

%N (Product(primitive roots of p) - 1)/p, where p = prime(n) and n > 2.

%C Gauss proved that the product of the primitive roots of p is congruent to 1 modulo p, for all primes p except p = 3.

%D C. F. Gauss, Disquisitiones Arithmeticae, Yale, 1965; see p. 52.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Primitive_root_modulo_n#Arithmetic_facts">Primitive root</a>

%F a(n) = (A123475(n) - 1)/A000040(n) for n > 2.

%e The primitive roots of prime(4) = 7 are 3 and 5, and (3*5 - 1)/7 = 14/7 = 2, so a(4) = 2.

%t a[n_] := With[{p = Prime[n]}, Select[Range[p - 1], MultiplicativeOrder[#, p] == p - 1 &]]; Table[(Product[ a[n][[i]], {i, Length[a[n]]}] - 1)/Prime[n], {n, 3, 20}]

%Y Cf. A060749, A088145, A123475.

%K nonn

%O 3,2

%A _Jonathan Sondow_, Feb 09 2013

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Last modified September 27 09:09 EDT 2020. Contains 337380 sequences. (Running on oeis4.)