A385603 Number of equivalence classes of Hurwitz quaternions of norm n with equivalence by left and right multiplication with units.

1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 3, 1, 4, 1, 2, 1, 4, 3, 4, 2, 3, 2, 4, 1, 4, 2, 4, 2, 5, 3, 6, 1, 4, 4, 5, 1, 7, 2, 4, 1, 7, 4, 6, 3, 5, 4, 6, 2, 8, 3, 5, 2, 7, 4, 10, 1, 8, 4, 7, 2, 8, 4, 6, 2, 8, 5, 11, 3, 8, 6, 8, 1, 11, 4, 7, 4, 10, 5, 10, 1, 8, 7, 12, 2, 12, 4, 10, 1, 10, 7, 13, 4, 9, 6, 10, 3, 16, 5, 9, 4, 11, 6, 14, 2, 10, 8, 12, 3, 17, 5, 12, 2, 12

Offset: 1

Author

R. J. Mathar, Aug 02 2025

Keywords

• nonn

Comments

Equivalence between Hurwitz quaternions q1 and q2 defined here: they are equivalent if units u1 and u2 exist such that q1 = u1* q2*u2. This is a relaxed requirement compared with A055672.

Links

• R. J. Mathar, Java program listing

Crossrefs

Cf. A000593 (equivalence defined by q1 = q2*u2), A055672 (primes in A000593).