A086087 a(n) is the minimal m such that the group GL(m,3) has an element of order n.

1, 2, 2, 4, 2, 6, 2, 4, 4, 5, 4, 3, 6, 6, 4, 16, 4, 18, 4, 8, 5, 11, 4

Offset: 2

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 24 2003

Keywords

• nonn
• more

Comments

For n > 2, a(prime(n)) = A062117(n). Also, for any n, a(n) <= n. - Eric M. Schmidt, May 18 2013

Crossrefs

Cf. A085430, A053290.

Programs

GAP

A086087 := function(n) local m; if IsPrime(n) and n>3 then return Order(3*Z(n)^0); fi; m := 1; while true do if ForAny(ConjugacyClasses(GL(m, 3)), cc->Order(Representative(cc))=n) then return m; fi; m := m + 1; od; end; # Eric M. Schmidt, May 18 2013

Extensions

Extended and corrected by Eric M. Schmidt, May 18 2013