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

1,3

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

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.

Prog

(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

Crossrefs

Cf. A035170, A091727.

Sequence in context: A357293 A357119 A357883 * A108069 A227837 A263099

Adjacent sequences: A091725 A091726 A091727 * A091729 A091730 A091731

Keyword

easy,nonn

Author

Paul Boddington, Feb 02 2004

Extensions

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

Status

approved