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

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, 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, 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

Offset: 1

Author

Paul Boddington, Feb 02 2004

Keywords

• easy
• nonn

Comments

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

References

• David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
• A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A035170, A091727.

Programs

PARI

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))); };
A091728(n) = if(!isA091727(n),0,(2-((2==n)||(5==n)||issquare(n)))); \\ Antti Karttunen, Feb 24 2020

Formula

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.

Extensions

Data section extended up to a(121) by Antti Karttunen, Feb 24 2020