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A118917 Number of inequivalent primes in ring of integers Z[sqrt(2)] with absolute value of norm = n.

%I A118917 #10 Aug 30 2017 15:16:30
%S A118917 0,0,1,0,0,0,0,2,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,2,0,1,0,0,0,0,0,2,0,0,
%T A118917 0,0,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A118917 0,0,0,2,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,2,0
%N A118917 Number of inequivalent primes in ring of integers Z[sqrt(2)] with absolute value of norm = n.
%C A118917 Since there are infinitely many units in Z[sqrt(2)], the total number of primes with a given norm is infinite (when there are any).
%H A118917 Antti Karttunen, <a href="/A118917/b118917.txt">Table of n, a(n) for n = 0..65537</a>
%F A118917 a(n) = 2 if n is a prime = 1,7 (mod 8); a(n) = 1 if n is 2 or p^2 where p is a prime = 3,5 (mod 8); otherwise a(n) = 0.
%t A118917 a[n_] := Which[PrimeQ[n] && MatchQ[Mod[n, 8], 1|7], 2, p = Sqrt[n]; n == 2 || IntegerQ[p] && PrimeQ[p] && MatchQ[Mod[p, 8], 3|5], 1, True, 0]; Table[a[n], {n, 0, 104}] (* _Jean-François Alcover_, Nov 22 2016 *)
%o A118917 (PARI) A118917(n) = { my(p); if(isprime(n)&&((1==(n%8))||(7==(n%8))), 2, if((2==n)||((issquare(n,&p)&&isprime(p))&&((3==(p%8))||(5==(p%8)))),1,0)); }; \\ _Antti Karttunen_, Aug 30 2017
%Y A118917 Cf. A055029, A118916.
%K A118917 easy,nice,nonn
%O A118917 0,8
%A A118917 _Franklin T. Adams-Watters_, May 05 2006