A055669 Number of prime Hurwitz quaternions of norm prime(n).

24, 96, 144, 192, 288, 336, 432, 480, 576, 720, 768, 912, 1008, 1056, 1152, 1296, 1440, 1488, 1632, 1728, 1776, 1920, 2016, 2160, 2352, 2448, 2496, 2592, 2640, 2736, 3072, 3168, 3312, 3360, 3600, 3648, 3792, 3936, 4032, 4176, 4320, 4368, 4608, 4656, 4752

Offset: 1

Author

N. J. A. Sloane, Jun 09 2000

Keywords

• nonn
• easy
• nice

Comments

Number of vectors of norm p in D_4 lattice (cf. A004011).

References

• L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• L. E. Dickson, Algebras and Their Arithmetics, Univ. of Chicago Press, 1923, Section 91 (page 147).

Crossrefs

Cf. A055670, A055671, A055672.

Cf. A240068 (number of prime Lipschitz quaternions having norm prime(n)).

Programs

Mathematica

Join[{24},24(#+1)&/@Prime[Range[2,50]]] (* Harvey P. Dale, Mar 12 2013 *)

Formula

a(n) = 24 * (prime(n)+1) = 24 * A008864(n) for n >= 2.

a(n) = 24*A055670(n).

a(n) = A004011(prime(n)). - R. J. Mathar, Aug 01 2025

Extensions

More terms from David W. Wilson, May 02 2001