cp's OEIS Frontend

A091728 Number of prime ideals of Z[sqrt(-5)] of norm n.

%I A091728 #10 Feb 24 2020 17:16:54
%S A091728 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 A091728 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 A091728 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 A091728 Number of prime ideals of Z[sqrt(-5)] of norm n.
%C A091728 It follows that the total number of ideals of norm n is A035170(n).
%D A091728 David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
%D A091728 A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.
%H A091728 Antti Karttunen, <a href="/A091728/b091728.txt">Table of n, a(n) for n = 1..65537</a>
%F A091728 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 A091728 (PARI)
%o A091728 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 A091728(n) = if(!isA091727(n),0,(2-((2==n)||(5==n)||issquare(n)))); \\ _Antti Karttunen_, Feb 24 2020
%Y A091728 Cf. A035170, A091727.
%K A091728 easy,nonn
%O A091728 1,3
%A A091728 _Paul Boddington_, Feb 02 2004
%E A091728 Data section extended up to a(121) by _Antti Karttunen_, Feb 24 2020