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

1,1

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).

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

Mathematica

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

Crossrefs

Cf. A055670, A055671, A055672.

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

Sequence in context: A057102 A376687 A057103 * A370846 A335144 A209432

Adjacent sequences: A055666 A055667 A055668 * A055670 A055671 A055672

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jun 09 2000

Extensions

More terms from David W. Wilson, May 02 2001

Status

approved