A385603 - OEIS

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

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OFFSET

1,7

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

Table of n, a(n) for n=1..121.

R. J. Mathar, Java program listing

CROSSREFS

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

Sequence in context: A175023 A128115 A091318 * A198898 A003639 A174110

Adjacent sequences: A385600 A385601 A385602 * A385604 A385605 A385606

KEYWORD

nonn

AUTHOR

R. J. Mathar, Aug 02 2025

STATUS

approved