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Number of prime ideals of Z[sqrt(-5)] of norm n.
3

%I #10 Feb 24 2020 17:16:54

%S 0,1,2,0,1,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,

%T 0,0,0,0,0,0,2,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,2,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,0,0,2,0,2,0,0,0,0,0,0,0,0,0,0,0,1

%N Number of prime ideals of Z[sqrt(-5)] of norm n.

%C It follows that the total number of ideals of norm n is A035170(n).

%D David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.

%D A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.

%H Antti Karttunen, <a href="/A091728/b091728.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n)=0 if n is not in A091727. If n is in A091727 and n is 2, 5 or a square then a(n)=1. Otherwise a(n)=2.

%o (PARI)

%o isA091727(n) = { my(ms = [1, 2, 3, 5, 7, 9], p, e=isprimepower(n,&p)); if(!e || e>2, 0, bitxor(e-1,!!vecsearch(ms,p%20))); };

%o A091728(n) = if(!isA091727(n),0,(2-((2==n)||(5==n)||issquare(n)))); \\ _Antti Karttunen_, Feb 24 2020

%Y Cf. A035170, A091727.

%K easy,nonn

%O 1,3

%A _Paul Boddington_, Feb 02 2004

%E Data section extended up to a(121) by _Antti Karttunen_, Feb 24 2020